Basic preset

Basic preset of tools to build more complex sets of tools later. More...

Files
file	Binormal.cl
	Compute the tangent vector in 2D sims, and the binormal in 3D sims.
file	deltaSPH.cl
	delta-SPH methods, including the correction terms
file	DensityClamp.cl
	Particles out of domain filter.
file	Domain.cl
	Particles out of domain filter.
file	EOS.cl
	Equation Of State (EOS) computation.
file	IdInverse.cl
	Permutations to move from the sorted indexes space to the unsorted one.
file	MLS.cl
	MLS kernel transformation matrix computation.
file	Coalesce.cl
	Splitting particles methods.
file	Cube.cl
	Splitting particles methods.
file	Remove.cl
	Set the mass of the particles according to the iterations since they were split/coalesced.
file	SetMass.cl
	Set the mass of the particles according to the iterations since they were split/coalesced.
file	Sort.cl
	Sort the multiresolution involved particle properties.
file	Sphere.cl
	Splitting particles methods.
file	Split.cl
	Splitting particles methods.
file	neighs.cl
	Compute the number of neighbours of each particle.
file	SetBuffer.cl
	Buffer particles identify and usage.
file	Shepard.cl
	Shepard renormalization factor computation.
file	Sort.cl
	Sort all the particle variables by the cell indexes.
file	adam_bashforth.cl
	Improved Euler time integration scheme.
file	euler.cl
	1st order Euler time integration scheme
file	improved_euler.cl
	Improved Euler time integration scheme.
file	midpoint.cl
	Semi-implicit Midpoint Euler time integration scheme.
file	deltaSPH.cl
	delta-SPH methods, including the correction terms
file	Shepard.cl
	Shepard renormalization factor computation, when variable kernel length is considered.
file	Sort.cl
	Sort all the particle variables by the cell indexes.
file	MLS.cl
	Shepard renormalization factor computation.
file	Shepard.cl
	Shepard renormalization factor computation.
file	Shepard.cl
	Shepard renormalization factor computation.

Macros
#define	EXCLUDED_PARTICLE(index)
	Condition to exclude a particle from the delta-SPH model.
#define	EXCLUDED_PARTICLE(index)
	Condition to exclude a particle from the EOS computation.
#define	M_ITERS   10
	Number of iterations to complete the mass transfer.
#define	CAPTURING_RADIUS   0.75f
#define	CAPTURING_RADIUS2   (CAPTURING_RADIUS + 0.01f)
#define	M_ITERS   10
	Number of iterations to complete the mass transfer.
#define	M_ITERS   10
	Number of iterations to complete the mass transfer.
#define	N_DAUGHTER   4
#define	M_ITERS   10
#define	EXCLUDED_PARTICLE(index)
	Excluded particles from the Shepard renormalization factor computation.
#define	TSCHEME_ADAMS_BASHFORTH_STEPS   5u
#define	DYDT_1(dydt_0)
#define	DYDT_2(dydt_0, dydt_1)
#define	DYDT_3(dydt_0, dydt_1, dydt_2)
#define	DYDT_4(dydt_0, dydt_1, dydt_2, dydt_3)
#define	DYDT_5(dydt_0, dydt_1, dydt_2, dydt_3, dydt_4)
#define	EXCLUDED_PARTICLE(index)
	Condition to exclude a particle from the delta-SPH model.
#define	EXCLUDED_PARTICLE(index)
	Excluded particles from the Shepard renormalization factor computation.

Functions
__kernel void	entry (const __global vec *normal, __global vec *tangent, __global vec *binormal, usize N)
	Compute the tanget vector in 2D simulations, and the binormal vector in 3D simulations.
__kernel void	simple (const __global unsigned int *iset, const __global int *imove, __global vec *lap_p_corr, __constant float *refd, usize N, vec g)
	Simple hidrostatic based correction term.
__kernel void	full (const __global int *imove, const __global vec *r, const __global float *rho, const __global float *m, const __global float *p, __global vec *lap_p_corr, usize N, LINKLIST_LOCAL_PARAMS)
	MLS based correction term.
__kernel void	full_mls (const __global int *imove, const __global matrix *mls, __global vec *lap_p_corr, usize N)
	MLS based correction term.
__kernel void	lapp (const __global int *imove, const __global vec *r, const __global float *rho, const __global float *m, const __global float *p, __global float *lap_p, usize N, LINKLIST_LOCAL_PARAMS)
	Laplacian of the pressure computation.
__kernel void	lapp_corr (const __global int *imove, const __global vec *r, const __global float *rho, const __global float *m, const __global vec *lap_p_corr, __global float *lap_p, usize N, LINKLIST_LOCAL_PARAMS)
	Laplacian of the pressure correction.
__kernel void	deltaSPH (const __global unsigned int *iset, const __global int *imove, const __global float *rho, const __global float *lap_p, __global float *drhodt, __constant float *refd, __constant float *delta, usize N, float dt)
	Density variation rates delta-SPH term.
__kernel void	entry (__global float *rho_in, usize N, float rho_min, float rho_max)
	Clamp the density.
__kernel void	entry (__global int *imove, __global vec *r_in, __global vec *u_in, __global vec *dudt_in, __global float *m, usize N, vec domain_min, vec domain_max)
	Check and destroy the particles out of the domain.
__kernel void	entry (__global unsigned int *iset, __global int *imove, __global float *rho, __global float *p, __constant float *refd, usize N, float cs, float p0)
	Stiff Equation Of State (EOS) computation.
__kernel void	entry (__global usize *id, __global usize *id_inverse, usize N)
	Compute the permutations to move from the sorted indexes space to the unsorted one.
__kernel void	entry (const __global int *imove, const __global vec *r, const __global float *rho, const __global float *m, __global matrix *mls, usize N, uint mls_imove, LINKLIST_LOCAL_PARAMS)
	Compute the MLS transformation matrix inverse, \( L_i^{-1} \).
__kernel void	mls_inv (const __global int *imove, __global matrix *mls, usize N, uint mls_imove)
	Invert the matrix computed in entry() to get the final MLS transformation matrix, \( L_i \).
__kernel void	seed_candidates (__global const unsigned int *iset, __global const int *imove, __global const unsigned int *ilevel, __global const unsigned int *level, __global const float *m0, __global int *miter, __global const vec *r, __global unsigned int *isplit, __global svec *split_cell, __global float *split_dist, __constant float *dr_level0, usize N)
	Look for all the seed candidates, i.e. all the particles which have a refinement level target lower than their current value.
__kernel void	seeds (__global const unsigned int *iset, __global const unsigned int *isplit_in, __global unsigned int *isplit, __global int *miter, __global const svec *split_cell, __global const float *split_dist, usize N, LINKLIST_LOCAL_PARAMS)
	Get only one seed per cell.
__kernel void	set_isplit_in (__global const unsigned int *isplit, __global unsigned int *isplit_in, usize N)
	Create a copy of isplit, where everything is 0 except the seeds, which take the value 1. Such array can be used to count the number of new particles to become generated.
__kernel void	children (__global const int *imove, __global const unsigned int *iset, __global const vec *r, __global const unsigned int *ilevel, __global unsigned int *isplit, __global int *miter, __constant float *dr_level0, usize N, LINKLIST_LOCAL_PARAMS)
	Look for all children, close enough to the seed.
__kernel void	weights (__global const unsigned int *iset, __global const unsigned int *ilevel, __global const vec *r, __global const unsigned int *isplit, __global float *split_weight, __constant float *dr_level0, usize N, LINKLIST_LOCAL_PARAMS)
	Compute the contribution weight of each children particle.
__kernel void	generate (__global int *imove, __global int *iset, __global const unsigned int *isplit, __global usize *split_invperm, __global unsigned int *ilevel, __global unsigned int *level, __global int *miter, __global usize *mybuffer, usize N, usize nbuffer)
	Associate a buffer particle to a seed.
__kernel void	fields (__global const unsigned int *iset, __global const uint *isplit, __global const usize *mybuffer, __global const unsigned int *ilevel, __global const float *split_weight, __global float *m0, __global float *m, __global vec *r, __global vec *u, __global vec *dudt, __global float *rho, __global float *drhodt, __constant float *dr_level0, usize N, LINKLIST_LOCAL_PARAMS)
	Collect the children, and the seed itself, in order to compute the field values of the buffer partner particle.
__kernel void	entry (__global const int *imove, __global const unsigned int *ilevel, __global const vec *r, __global unsigned int *level, usize N, vec multiresolution_cube_min, vec multiresolution_cube_max, unsigned int multiresolution_cube_level)
	Set the refinement level of the particles inside.
__kernel void	entry (__global int *imove, __global const int *miter, __global vec *r, vec domain_max, usize N)
	Set the mass of the particles according to their gamma value.
__kernel void	set_mass (__global const int *imove, __global const float *m0, __global int *miter, __global float *m, usize N)
	Set the mass of the particles according to their gamma value.
__kernel void	entry (const __global float *m0_in, __global float *m0, const __global int *miter_in, __global int *miter, const __global uint *ilevel_in, __global uint *ilevel, const __global uint *level_in, __global uint *level, const __global usize *id_sorted, usize N)
	Sort the multiresolution involved particle properties.
__kernel void	entry (__global const int *imove, __global const unsigned int *ilevel, __global const vec *r, __global unsigned int *level, usize N, vec multiresolution_sphere_center, float multiresolution_sphere_radius, unsigned int multiresolution_sphere_level)
	Set the refinement level of the particles inside.
__kernel void	check_split (__global const int *imove, __global const float *m, __global const int *miter, __global const unsigned int *ilevel, __global const unsigned int *level, __global unsigned int *isplit, usize N)
	Check and store wether a particle should become split or not.
__kernel void	generate (__global int *imove, __global int *iset, __global unsigned int *isplit, __global usize *split_invperm, __global unsigned int *ilevel, __global unsigned int *level, __global float *m0, __global int *miter, __global float *m, __global vec *r, __global vec *u, __global vec *dudt, __global float *rho, __global float *drhodt, usize N, usize nbuffer)
	Split a particle in a set of daughter particles.
__kernel void	entry (const __global int *imove, __global uint *n_neighs, uint neighs_limit, usize N, LINKLIST_LOCAL_PARAMS)
	Number of neighbours of each particle.
__kernel void	count (__global const int *imove, __global unsigned int *ibuffer, usize N)
	Identify the buffer particles.
__kernel void	set_imove (__global int *imove, usize N)
	Replace the particles with the imove flag imove=-256 by imove=-255.
__kernel void	entry (const __global int *imove, const __global vec *r, const __global float *rho, const __global float *m, __global float *shepard, usize N, LINKLIST_LOCAL_PARAMS)
	Shepard factor computation.
__kernel void	stage1 (const __global usize *id_in, __global usize *id, const __global uint *iset_in, __global uint *iset, const __global int *imove_in, __global int *imove, const __global vec *r_in, __global vec *r, const __global vec *normal_in, __global vec *normal, const __global vec *tangent_in, __global vec *tangent, const __global usize *id_sorted, usize N)
	Sort all the particle variables by the cell indexes.
__kernel void	stage2 (const __global float *rho_in, __global float *rho, const __global float *m_in, __global float *m, const __global vec *u_in, __global vec *u, const __global vec *dudt, __global vec *dudt_in, const __global float *drhodt, __global float *drhodt_in, const __global usize *id_sorted, usize N)
	Sort all the particle variables by the cell indexes.
__kernel void	predictor (__global vec *r, __global vec *u, __global vec *dudt, __global float *rho, __global float *drhodt, __global vec *r_in, __global vec *u_in, __global vec *dudt_in, __global float *rho_in, __global float *drhodt_in, usize N)
	Adams-Bashforth time integration scheme predictor stage.
__kernel void	sort (const __global vec *dudt_as1_in, __global vec *dudt_as1, const __global vec *dudt_as2_in, __global vec *dudt_as2, const __global vec *dudt_as3_in, __global vec *dudt_as3, const __global vec *dudt_as4_in, __global vec *dudt_as4, const __global float *drhodt_as1_in, __global float *drhodt_as1, const __global float *drhodt_as2_in, __global float *drhodt_as2, const __global float *drhodt_as3_in, __global float *drhodt_as3, const __global float *drhodt_as4_in, __global float *drhodt_as4, const __global usize *id_sorted, usize N)
	Sort the stored Adams-Bashforth stored variation rates.
__kernel void	corrector (__global int *imove, __global unsigned int *iset, __global vec *r, __global vec *u, __global vec *dudt, __global float *rho, __global float *drhodt, __global vec *dudt_as1, __global float *drhodt_as1, __global vec *dudt_as2, __global float *drhodt_as2, __global vec *dudt_as3, __global float *drhodt_as3, __global vec *dudt_as4, __global float *drhodt_as4, usize N, float dt, unsigned int iter)
	Improved Euler time integration scheme corrector stage.
__kernel void	postcorrector (const __global vec *dudt_as1, const __global float *drhodt_as1, const __global vec *dudt_as2, const __global float *drhodt_as2, const __global vec *dudt_as3, const __global float *drhodt_as3, const __global vec *dudt, const __global float *drhodt, __global vec *dudt_as1_in, __global float *drhodt_as1_in, __global vec *dudt_as2_in, __global float *drhodt_as2_in, __global vec *dudt_as3_in, __global float *drhodt_as3_in, __global vec *dudt_as4_in, __global float *drhodt_as4_in, usize N)
	Backup de data for the sorting algorithm.
__kernel void	corrector (__global int *imove, __global unsigned int *iset, __global vec *r, __global vec *u, __global vec *dudt, __global float *rho, __global float *drhodt, usize N, float dt)
	1st orderv Euler time integration scheme corrector stage
__kernel void	predictor (__global int *imove, __global vec *r, __global vec *u, __global vec *dudt, __global float *rho, __global float *drhodt, __global vec *r_in, __global vec *u_in, __global vec *dudt_in, __global float *rho_in, __global float *drhodt_in, usize N, float dt)
	Improved Euler time integration scheme predictor stage.
__kernel void	corrector (__global int *imove, __global unsigned int *iset, __global vec *r, __global vec *u, __global vec *dudt, __global float *rho, __global float *drhodt, __global vec *dudt_in, __global float *drhodt_in, usize N, float dt)
	Improved Euler time integration scheme corrector stage.
__kernel void	predictor (const __global vec *r, const __global vec *u, const __global vec *dudt, const __global float *rho, const __global float *drhodt, __global vec *r_in, __global vec *u_in, __global vec *dudt_in, __global float *rho_in, __global float *drhodt_in, usize N)
	Semi-implicit Midpoint Euler time integration scheme predictor stage.
__kernel void	midpoint (const __global int *imove, const __global vec *u_in, __global vec *u, const __global vec *dudt, const __global float *rho_in, __global float *rho, const __global float *drhodt, usize N, float dt)
	Advance to the time step midpoint.
__kernel void	midpoint_r (const __global int *imove, const __global vec *r_in, __global vec *r, const __global vec *u, usize N, float dt)
	Advance the position to the time step midpoint.
__kernel void	relax (const __global int *imove, __global vec *dudt_in, __global vec *dudt, __global float *drhodt_in, __global float *drhodt, usize N, float relax_midpoint)
__kernel void	residuals (const __global int *imove, const __global float *m, const __global vec *u, const __global vec *dudt_in, const __global vec *dudt, const __global float *rho, const __global float *p, const __global float *drhodt_in, const __global float *drhodt, __global float *residual_midpoint, usize N)
__kernel void	corrector (const __global int *imove, const __global vec *r_in, __global vec *r, const __global vec *u_in, __global vec *u, const __global vec *dudt, const __global float *rho_in, __global float *rho, const __global float *drhodt, usize N, float dt)
	1st order Semi-implicit Euler time integration scheme corrector stage
__kernel void	lapp (const __global int *imove, const __global vec *r, const __global float *rho, const __global float *m, const __global float *p, const __global float *h_var, __global float *lap_p, usize N, LINKLIST_LOCAL_PARAMS)
	Laplacian of the pressure computation.
__kernel void	entry (const __global int *imove, const __global vec *r, const __global float *rho, const __global float *m, const __global float *h_var, __global float *shepard, usize N, LINKLIST_LOCAL_PARAMS)
	Shepard factor computation.
__kernel void	entry (const __global float *h_var_in, __global float *h_var, const __global usize *id_sorted, usize N)
	Sort all the particle variables by the cell indexes.
__kernel void	entry (const __global int *imove, const __global int *imirrored, const __global vec *r, const __global float *rho, const __global float *m, __global matrix *mls, usize N, uint mls_imove, LINKLIST_LOCAL_PARAMS)
	Compute the MLS transformation matrix inverse, \( L_i^{-1} \), due to the particles at the other portal side.
__kernel void	entry (const __global int *imove, const __global int *imirrored, const __global vec *r, const __global float *rho, const __global float *m, __global float *shepard, usize N, LINKLIST_LOCAL_PARAMS)
	Shepard factor computation, due to the particles at the other portal side.
__kernel void	entry (const __global int *imove, const __global int *imirrored, const __global vec *r, const __global float *rho, const __global float *m, const __global float *h_var, __global float *shepard, usize N, LINKLIST_LOCAL_PARAMS)
	Shepard factor computation, due to the particles at the other portal side.

Detailed Description

Basic preset of tools to build more complex sets of tools later.

Macro Definition Documentation

CAPTURING_RADIUS

#define CAPTURING_RADIUS   0.75f

CAPTURING_RADIUS2

#define CAPTURING_RADIUS2   (CAPTURING_RADIUS + 0.01f)

DYDT_1

#define DYDT_1

(

dydt_0

)

Value:

dydt_0

DYDT_2

#define DYDT_2	(		dydt_0,
			dydt_1 )

Value:

1.5f * dydt_0 - 0.5f * dydt_1

DYDT_3

#define DYDT_3	(		dydt_0,
			dydt_1,
			dydt_2 )

Value:

    23.f / 12.f * dydt_0 - 4.f / 3.f * dydt_1 + 5.f / 12.f * dydt_2

DYDT_4

#define DYDT_4	(		dydt_0,
			dydt_1,
			dydt_2,
			dydt_3 )

Value:

    55.f / 24.f * dydt_0 - 59.f / 24.f * dydt_1 + 37.f / 24.f * dydt_2 - \
    3.f / 8.f * dydt_3

DYDT_5

#define DYDT_5	(		dydt_0,
			dydt_1,
			dydt_2,
			dydt_3,
			dydt_4 )

Value:

    1901.f / 720.f * dydt_0 - 1387.f / 360.f * dydt_1 + 109.f / 30.f * dydt_2 - \
    637.f / 360.f * dydt_3 + 251.f / 720.f * dydt_4

EXCLUDED_PARTICLE [1/5]

#define EXCLUDED_PARTICLE

(

index

)

Value:

imove[index] <= 0

Condition to exclude a particle from the delta-SPH model.

Excluded particles from the Shepard renormalization factor computation.

Condition to exclude a particle from the EOS computation.

By default all the boundary elements are excluded. Even though it is enough for simulation where fluid and solid mechanics are not combined, it is strongly recommended to conveniently overload this macro.

Note

Redefining this macro this OpenCL script can be recicled

By default all the boundary elements are excluded, excepting the fixed particles (imove = -1)

Note

Redefining this macro this OpenCL script can be recicled for different particle types.

By default all the particles are included. Therefore it is strongly recommended to redefine this macro to specify whether the fluid particles (imove != 1) or the solid particles (imove != 2) are used

Note

Redefining this macro this OpenCL script can be recicled

Remarks

The Shepard renormalization factor is ever computed at the boundary elements and sensors (imove <= 0)

EXCLUDED_PARTICLE [2/5]

#define EXCLUDED_PARTICLE

(

index

)

Value:

(imove[index] <= 0) && (imove[index] != -1)

Condition to exclude a particle from the EOS computation.

Condition to exclude a particle from the delta-SPH model.

Excluded particles from the Shepard renormalization factor computation.

By default all the boundary elements are excluded, excepting the fixed particles (imove = -1)

Note

Redefining this macro this OpenCL script can be recicled for different particle types.

By default all the particles are included. Therefore it is strongly recommended to redefine this macro to specify whether the fluid particles (imove != 1) or the solid particles (imove != 2) are used

Note

Redefining this macro this OpenCL script can be recicled

Remarks

The Shepard renormalization factor is ever computed at the boundary elements and sensors (imove <= 0)

By default all the boundary elements are excluded. Even though it is enough for simulation where fluid and solid mechanics are not combined, it is strongly recommended to conveniently overload this macro.

Note

Redefining this macro this OpenCL script can be recicled

EXCLUDED_PARTICLE [3/5]

#define EXCLUDED_PARTICLE

(

index

)

Value:

imove[index] >= 3

Excluded particles from the Shepard renormalization factor computation.

Condition to exclude a particle from the delta-SPH model.

By default all the particles are included. Therefore it is strongly recommended to redefine this macro to specify whether the fluid particles (imove != 1) or the solid particles (imove != 2) are used

Note

Redefining this macro this OpenCL script can be recicled

Remarks

The Shepard renormalization factor is ever computed at the boundary elements and sensors (imove <= 0)

By default all the boundary elements are excluded. Even though it is enough for simulation where fluid and solid mechanics are not combined, it is strongly recommended to conveniently overload this macro.

Note

Redefining this macro this OpenCL script can be recicled

EXCLUDED_PARTICLE [4/5]

#define EXCLUDED_PARTICLE

(

index

)

Value:

imove[index] <= 0

Condition to exclude a particle from the delta-SPH model.

Excluded particles from the Shepard renormalization factor computation.

By default all the boundary elements are excluded. Even though it is enough for simulation where fluid and solid mechanics are not combined, it is strongly recommended to conveniently overload this macro.

Note

Redefining this macro this OpenCL script can be recicled

By default all the particles are included. Therefore it is strongly recommended to redefine this macro to specify whether the fluid particles (imove != 1) or the solid particles (imove != 2) are used

Note

Redefining this macro this OpenCL script can be recicled

Remarks

The Shepard renormalization factor is ever computed at the boundary elements and sensors (imove <= 0)

EXCLUDED_PARTICLE [5/5]

#define EXCLUDED_PARTICLE

(

index

)

Value:

imove[index] >= 3

Excluded particles from the Shepard renormalization factor computation.

By default all the particles are included. Therefore it is strongly recommended to redefine this macro to specify whether the fluid particles (imove != 1) or the solid particles (imove != 2) are used

Note

Redefining this macro this OpenCL script can be recicled

Remarks

The Shepard renormalization factor is ever computed at the boundary elements and sensors (imove <= 0)

M_ITERS [1/4]

#define M_ITERS   10

Number of iterations to complete the mass transfer.

When a particle is split or coalesced, its mass is not inmediately removed, but a smooth transition is carried out

M_ITERS [2/4]

#define M_ITERS   10

Number of iterations to complete the mass transfer.

When a particle is split or coalesced, its mass is not inmediately removed, but a smooth transition is carried out

M_ITERS [3/4]

#define M_ITERS   10

Number of iterations to complete the mass transfer.

When a particle is split or coalesced, its mass is not inmediately removed, but a smooth transition is carried out

M_ITERS [4/4]

#define M_ITERS   10

N_DAUGHTER

#define N_DAUGHTER   4

TSCHEME_ADAMS_BASHFORTH_STEPS

#define TSCHEME_ADAMS_BASHFORTH_STEPS   5u

Function Documentation

check_split()

__kernel void check_split	(	__global const int *	imove,
		__global const float *	m,
		__global const int *	miter,
		__global const unsigned int *	ilevel,
		__global const unsigned int *	level,
		__global unsigned int *	isplit,
		usize	N )

Check and store wether a particle should become split or not.

A particle should be split if the target refinement level is bigger than its current one, and it is not already spliting/coalescing.

Parameters

imove	Moving flags. imove > 0 for regular fluid/solid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
m	Current mass \( m \).
miter	Mass transfer iteration (Positive for growing particles, negative for shrinking particles).
ilevel	Current refinement level of the particle.
level	Target refinement level of the particle.
isplit	0 if the particle should not become split, 1 otherwise
N	Number of particles.

children()

__kernel void children	(	__global const int *	imove,
		__global const unsigned int *	iset,
		__global const vec *	r,
		__global const unsigned int *	ilevel,
		__global unsigned int *	isplit,
		__global int *	miter,
		__constant float *	dr_level0,
		usize	N,
		LINKLIST_LOCAL_PARAMS	)

Look for all children, close enough to the seed.

When a particle is not already splitting or coalescing, and is close enough to one or more seeds (which should has the same refinement level and belongs to the same particles set), then it is marked as coalescing child.

Hence, since a particle may be close enough to several partner particles, later we should compute contribution weights.

Parameters

imove	Moving flags. imove > 0 for regular fluid/solid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
iset	Set of particles index.
r	Position \( \mathbf{r} \).
ilevel	Current refinement level of the particle.
isplit	0 if the particle should not become coalesced, 1 for the coalescing particles, 2 for the seeds.
miter	Mass transfer iteration (Positive for growing particles, negative for shrinking particles).
icell	Cell where each particle is located.
ihoc	Head of chain for each cell (first particle found).
dr_level0	Theoretical distance between particles at the lowest refinement level.
N	Number of particles.
n_cells	Number of cells in each direction

corrector() [1/4]

__kernel void corrector	(	__global int *	imove,
		__global unsigned int *	iset,
		__global vec *	r,
		__global vec *	u,
		__global vec *	dudt,
		__global float *	rho,
		__global float *	drhodt,
		__global vec *	dudt_as1,
		__global float *	drhodt_as1,
		__global vec *	dudt_as2,
		__global float *	drhodt_as2,
		__global vec *	dudt_as3,
		__global float *	drhodt_as3,
		__global vec *	dudt_as4,
		__global float *	drhodt_as4,
		usize	N,
		float	dt,
		unsigned int	iter )

Improved Euler time integration scheme corrector stage.

Parameters

imove	Moving flags. imove > 0 for regular fluid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
iset	Set of particles index.
r	Position \( \mathbf{r}_{n+1/2} \).
u	Velocity \( \mathbf{u}_{n+1/2} \).
dudt	Velocity rate of change \( \left. \frac{d \mathbf{u}}{d t} \right\vert_{n+1/2} \).
rho	Density \( \rho_{n+1/2} \).
drhodt	Density rate of change \( \left. \frac{d \rho}{d t} \right\vert_{n+1/2} \).
dudt_as1	Velocity rate of change of previous step \( \left. \frac{d \mathbf{u}}{d t} \right\vert_{n-1/2} \).
drhodt_as1	Density rate of change of previous step \( \left. \frac{d \rho}{d t} \right\vert_{n-1/2} \).
N	Number of particles.
dt	Time step \( \Delta t \).
iter	Current iteration.

corrector() [2/4]

__kernel void corrector	(	__global int *	imove,
		__global unsigned int *	iset,
		__global vec *	r,
		__global vec *	u,
		__global vec *	dudt,
		__global float *	rho,
		__global float *	drhodt,
		__global vec *	dudt_in,
		__global float *	drhodt_in,
		usize	N,
		float	dt )

Improved Euler time integration scheme corrector stage.

Parameters

imove	Moving flags. imove > 0 for regular fluid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
iset	Set of particles index.
r	Position \( \mathbf{r}_{n+1/2} \).
u	Velocity \( \mathbf{u}_{n+1/2} \).
dudt	Velocity rate of change \( \left. \frac{d \mathbf{u}}{d t} \right\vert_{n+1/2} \).
rho	Density \( \rho_{n+1/2} \).
drhodt	Density rate of change \( \left. \frac{d \rho}{d t} \right\vert_{n+1/2} \).
dudt_in	Velocity rate of change \( \left. \frac{d \mathbf{u}}{d t} \right\vert_{n-1/2} \).
drhodt_in	Density rate of change \( \left. \frac{d \rho}{d t} \right\vert_{n-1/2} \).
N	Number of particles.
dt	Time step \( \Delta t \).

corrector() [3/4]

__kernel void corrector	(	__global int *	imove,
		__global unsigned int *	iset,
		__global vec *	r,
		__global vec *	u,
		__global vec *	dudt,
		__global float *	rho,
		__global float *	drhodt,
		usize	N,
		float	dt )

1st orderv Euler time integration scheme corrector stage

Parameters

imove	Moving flags. imove > 0 for regular fluid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
iset	Set of particles index.
r	Position \( \mathbf{r}_{n+1/2} \).
u	Velocity \( \mathbf{u}_{n+1/2} \).
dudt	Velocity rate of change \( \left. \frac{d \mathbf{u}}{d t} \right\vert_{n+1/2} \).
rho	Density \( \rho_{n+1/2} \).
drhodt	Density rate of change \( \left. \frac{d \rho}{d t} \right\vert_{n+1/2} \).
N	Number of particles.
dt	Time step \( \Delta t \).

corrector() [4/4]

__kernel void corrector	(	const __global int *	imove,
		const __global vec *	r_in,
		__global vec *	r,
		const __global vec *	u_in,
		__global vec *	u,
		const __global vec *	dudt,
		const __global float *	rho_in,
		__global float *	rho,
		const __global float *	drhodt,
		usize	N,
		float	dt )

1st order Semi-implicit Euler time integration scheme corrector stage

Parameters

imove	Moving flags. imove > 0 for regular fluid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
r_in	Position \( \mathbf{r}_{n} \).
r	Position \( \mathbf{r}_{n+1} \).
u_in	Velocity \( \mathbf{u}_{n} \).
u	Velocity \( \mathbf{u}_{n+1} \).
dudt	Velocity rate of change \( \left. \frac{d \mathbf{u}}{d t} \right\vert_{n+1/2} \).
rho_in	Density \( \rho_{n} \).
rho	Density \( \rho_{n+1} \).
drhodt	Density rate of change \( \left. \frac{d \rho}{d t} \right\vert_{n+1/2} \).
N	Number of particles.
dt	Time step \( \Delta t \).

count()

__kernel void count	(	__global const int *	imove,
		__global unsigned int *	ibuffer,
		usize	N )

Identify the buffer particles.

The buffer particles are signaled with an imove=-255 flag.

Parameters

imove	Moving flags (imove = -255 for buffer particles).
ibuffer	0 if the particle is not a buffer particle, 1 otherwise.
N	Number of particles.

deltaSPH()

__kernel void deltaSPH	(	const __global unsigned int *	iset,
		const __global int *	imove,
		const __global float *	rho,
		const __global float *	lap_p,
		__global float *	drhodt,
		__constant float *	refd,
		__constant float *	delta,
		usize	N,
		float	dt )

Density variation rates delta-SPH term.

Parameters

iset	Set of particles index.
imove	Moving flags. imove = 2 for regular solid particles. imove = 0 for sensors (ignored by this preset). imove < 0 for boundary elements/particles.
rho	Density \( \rho_{n+1} \).
lap_p	Pressure laplacian \( \Delta p \).
drhodt	Density rate of change \( \frac{d \rho}{d t} \).
refd	Density of reference of the fluid \( \rho_0 \).
delta	Diffusive term \( \delta \) multiplier.
N	Number of particles.
dt	Time step \( \Delta t \).

entry() [1/17]

__kernel void entry	(	__global const int *	imove,
		__global const unsigned int *	ilevel,
		__global const vec *	r,
		__global unsigned int *	level,
		usize	N,
		vec	multiresolution_cube_min,
		vec	multiresolution_cube_max,
		unsigned int	multiresolution_cube_level )

Set the refinement level of the particles inside.

Parameters

imove	Moving flags. imove > 0 for regular fluid/solid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
ilevel	Current refinement level of the particle.
r	Position \( \mathbf{r} \).
level	Target refinement level of the particle.
N	Number of particles.
multiresolution_cube_min	Minimum point of the refinement area.
multiresolution_cube_max	Maximum point of the refinement area.
multiresolution_cube_level	Refinement level inside the area.

entry() [2/17]

__kernel void entry	(	__global const int *	imove,
		__global const unsigned int *	ilevel,
		__global const vec *	r,
		__global unsigned int *	level,
		usize	N,
		vec	multiresolution_sphere_center,
		float	multiresolution_sphere_radius,
		unsigned int	multiresolution_sphere_level )

Set the refinement level of the particles inside.

Parameters

imove	Moving flags. imove > 0 for regular fluid/solid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
ilevel	Current refinement level of the particle.
r	Position \( \mathbf{r} \).
level	Target refinement level of the particle.
N	Number of particles.
multiresolution_sphere_center	Center of the refinement area.
multiresolution_sphere_radius	Radius of the refinement area.
multiresolution_sphere_level	Refinement level inside the area.

entry() [3/17]

__kernel void entry	(	__global float *	rho_in,
		usize	N,
		float	rho_min,
		float	rho_max )

Clamp the density.

In some situations it can be convenient to define a minimum or maximum density values in order to avoid that a crazy particle may cause the simulation blow up. Use this tool only if you know exactly what you are doing

Parameters

rho_in	Density \( \rho_{n+1/2} \).
N	Number of particles.
rho_min	Minimum tolerated density value \( \rho_{min} \).
rho_max	Maximum tolerated density value \( \rho_{max} \).

entry() [4/17]

__kernel void entry	(	__global int *	imove,
		__global const int *	miter,
		__global vec *	r,
		vec	domain_max,
		usize	N )

Set the mass of the particles according to their gamma value.

When a particle is split in a set of daughter particles, in order to avoid shocks, its effect is smoothly transfered to the daughters, using for that a \( \gamma_m \) mass multiplier.

Parameters

imove	Moving flags. imove > 0 for regular fluid/solid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
miter	Mass transfer iteration (Positive for growing particles, negative for shrinking particles).
r	Position \( \mathbf{r} \).
domain_max	Maximum point of the computational domain.
N	Number of particles.

entry() [5/17]

__kernel void entry	(	__global int *	imove,
		__global vec *	r_in,
		__global vec *	u_in,
		__global vec *	dudt_in,
		__global float *	m,
		usize	N,
		vec	domain_min,
		vec	domain_max )

Check and destroy the particles out of the domain.

Usually is a good methodology to impose a computational domain, such that a single lost particle will not cause the simulation blow up. Since the particles out of the domain will take 0 mass, you can control how many particles are lost controlling the total mass

Parameters

imove	Moving flags. imove > 0 for regular fluid/solid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
r_in	Position \( \mathbf{r} \).
u_in	Velocity \( \mathbf{u} \).
dudt_in	Velocity rate of change \( \frac{d \mathbf{u}}{d t} \).
m	Mass \( m \).
N	Number of particles.
domain_min	Minimum point of the domain.
domain_max	Maximum point of the domain.

entry() [6/17]

__kernel void entry	(	__global unsigned int *	iset,
		__global int *	imove,
		__global float *	rho,
		__global float *	p,
		__constant float *	refd,
		usize	N,
		float	cs,
		float	p0 )

Stiff Equation Of State (EOS) computation.

The equation of state relates the pressure and the density fields, \( p = p_0 + c_s^2 \left(\rho - \rho_0 \right) \)

Parameters

iset	Set of particles index.
imove	Moving flags. imove > 0 for regular fluid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
rho	Density \( \rho_{n+1/2} \).
p	Pressure \( p_{n+1/2} \).
refd	Density of reference of the fluid \( \rho_0 \).
N	Number of particles.
cs	Speed of sound \( c_s \).
p0	Background pressure \( p_0 \).

entry() [7/17]

__kernel void entry	(	__global usize *	id,
		__global usize *	id_inverse,
		usize	N )

Compute the permutations to move from the sorted indexes space to the unsorted one.

Parameters

id	Original index of each particle (sort -> unsort space)
id_inverse	Sorted index of each particle (unsort -> sort space)
N	Number of particles.

entry() [8/17]

__kernel void entry	(	const __global float *	h_var_in,
		__global float *	h_var,
		const __global usize *	id_sorted,
		usize	N )

Sort all the particle variables by the cell indexes.

Due to the large number of registers consumed (21 global memory arrays are loaded), it is safer carrying out the sorting process in to stages. This is the first stage.

Parameters

h_var_in	Unsorted variable kernel lenght \( h \).
h_var	Sorted variable kernel lenght \( h \).
id_sorted	Permutations list from the unsorted space to the sorted one.
N	Number of particles.

entry() [9/17]

__kernel void entry	(	const __global float *	m0_in,
		__global float *	m0,
		const __global int *	miter_in,
		__global int *	miter,
		const __global uint *	ilevel_in,
		__global uint *	ilevel,
		const __global uint *	level_in,
		__global uint *	level,
		const __global usize *	id_sorted,
		usize	N )

Sort the multiresolution involved particle properties.

Parameters

m0_in	Unsorted original mass \( m_0 \).
m0	Sorted original mass \( m_0 \).
miter_in	Unsorted iteration of the mass transfer.
miter	Mass transfer iteration (Positive for shrinking particles, negative for growing particles).
ilevel_in	Unsorted particle refinement level.
ilevel	Sorted particle refinement level.
level_in	Unsorted target refinement level.
level	Sorted target refinement level.
id_sorted	Permutations list from the unsorted space to the sorted one.
N	Number of particles.

entry() [10/17]

__kernel void entry	(	const __global int *	imove,
		__global uint *	n_neighs,
		uint	neighs_limit,
		usize	N,
		LINKLIST_LOCAL_PARAMS	)

Number of neighbours of each particle.

One of the main targets of this kernel is checking that the number of neighbours is not excessively large. Along this line, if #neighs_limit neighbours are reached, the kernel will stop the execution.

Parameters

imove	Moving flags. imove > 0 for regular fluid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
r	Position \( \mathbf{r} \).
n_neighs	Number of neighbours per particle.
icell	Cell where each particle is located.
ihoc	Head of chain for each cell (first particle found).
neighs_limit	The largest number of neighbours accepted.
N	Number of particles.
n_cells	Number of cells in each direction

entry() [11/17]

__kernel void entry	(	const __global int *	imove,
		const __global int *	imirrored,
		const __global vec *	r,
		const __global float *	rho,
		const __global float *	m,
		__global float *	shepard,
		usize	N,
		LINKLIST_LOCAL_PARAMS	)

Shepard factor computation, due to the particles at the other portal side.

\[ \gamma(\mathbf{x}) = \int_{\Omega} W(\mathbf{y} - \mathbf{x}) \mathrm{d}\mathbf{x} \]

The shepard renormalization factor is applied for several purposes:

• To interpolate values
• To recover the consistency with the Boundary Integrals formulation
• Debugging

In the shepard factor computation the fluid extension particles are not taken into account.

Parameters

imove	Moving flags. imove > 0 for regular fluid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
imirrored	0 if the particle has not been mirrored, 1 otherwise.
r	Position \( \mathbf{r} \).
rho	Density \( \rho \).
m	Mass \( m \).
shepard	Shepard term \( \gamma(\mathbf{x}) = \int_{\Omega} W(\mathbf{y} - \mathbf{x}) \mathrm{d}\mathbf{x} \).
icell	Cell where each particle is located.
ihoc	Head of chain for each cell (first particle found).
N	Number of particles.
n_cells	Number of cells in each direction

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entry() [12/17]

__kernel void entry	(	const __global int *	imove,
		const __global int *	imirrored,
		const __global vec *	r,
		const __global float *	rho,
		const __global float *	m,
		__global matrix *	mls,
		usize	N,
		uint	mls_imove,
		LINKLIST_LOCAL_PARAMS	)

Compute the MLS transformation matrix inverse, \( L_i^{-1} \), due to the particles at the other portal side.

Such transformation matrix can be multiplied by the kernel gradient to produce a new kernel gradient, \( \nabla W^{L}_{ij} = L_i \cdot \nabla W_{ij} \), such that the lienar fields differential operators are consistently computed.

Parameters

imove	Moving flags. imove > 0 for regular fluid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
imirrored	0 if the particle has not been mirrored, 1 otherwise.
r	Position \( \mathbf{r} \).
rho	Density \( \rho \).
m	Mass \( m \).
mls	Kernel MLS transformation matrix \( L \).
icell	Cell where each particle is located.
ihoc	Head of chain for each cell (first particle found).
N	Number of particles.
n_cells	Number of cells in each direction
mls_imove	Type of particles affected

Note

The MLS kernel transformation will be computed just for the particles with the moving flag mls_imove, and using just the information of the particles with the moving flag mls_imove

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entry() [13/17]

__kernel void entry	(	const __global int *	imove,
		const __global int *	imirrored,
		const __global vec *	r,
		const __global float *	rho,
		const __global float *	m,
		const __global float *	h_var,
		__global float *	shepard,
		usize	N,
		LINKLIST_LOCAL_PARAMS	)

Shepard factor computation, due to the particles at the other portal side.

\[ \gamma(\mathbf{x}) = \int_{\Omega} W(\mathbf{y} - \mathbf{x}) \mathrm{d}\mathbf{x} \]

The shepard renormalization factor is applied for several purposes:

• To interpolate values
• To recover the consistency with the Boundary Integrals formulation
• Debugging

In the shepard factor computation the fluid extension particles are not taken into account.

Parameters

imove	Moving flags. imove > 0 for regular fluid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
imirrored	0 if the particle has not been mirrored, 1 otherwise.
r	Position \( \mathbf{r} \).
rho	Density \( \rho \).
m	Mass \( m \).
h_var	variable kernel lenght \( h \).
shepard	Shepard term \( \gamma(\mathbf{x}) = \int_{\Omega} W(\mathbf{y} - \mathbf{x}) \mathrm{d}\mathbf{x} \).
icell	Cell where each particle is located.
ihoc	Head of chain for each cell (first particle found).
N	Number of particles.
n_cells	Number of cells in each direction

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entry() [14/17]

__kernel void entry	(	const __global int *	imove,
		const __global vec *	r,
		const __global float *	rho,
		const __global float *	m,
		__global float *	shepard,
		usize	N,
		LINKLIST_LOCAL_PARAMS	)

Shepard factor computation.

\[ \gamma(\mathbf{x}) = \int_{\Omega} W(\mathbf{y} - \mathbf{x}) \mathrm{d}\mathbf{y} \]

The shepard renormalization factor is applied for several purposes:

• To interpolate values
• To recover the consistency with the Boundary Integrals formulation
• Debugging

In the shepard factor computation the fluid extension particles are not taken into account.

Parameters

imove	Moving flags. imove > 0 for regular fluid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
r	Position \( \mathbf{r} \).
rho	Density \( \rho \).
m	Mass \( m \).
shepard	Shepard term \( \gamma(\mathbf{x}) = \int_{\Omega} W(\mathbf{y} - \mathbf{x}) \mathrm{d}\mathbf{y} \).
icell	Cell where each particle is located.
ihoc	Head of chain for each cell (first particle found).
N	Number of particles.
n_cells	Number of cells in each direction

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entry() [15/17]

__kernel void entry	(	const __global int *	imove,
		const __global vec *	r,
		const __global float *	rho,
		const __global float *	m,
		__global matrix *	mls,
		usize	N,
		uint	mls_imove,
		LINKLIST_LOCAL_PARAMS	)

Compute the MLS transformation matrix inverse, \( L_i^{-1} \).

Such transformation matrix can be multiplied by the kernel gradient to produce a new kernel gradient, \( \nabla W^{L}_{ij} = L_i \cdot \nabla W_{ij} \), such that the lienar fields differential operators are consistently computed.

Parameters

imove	Moving flags. imove > 0 for regular fluid/solid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
r	Position \( \mathbf{r}_{n+1} \).
rho	Density \( \rho \).
m	Mass \( m \).
mls	Kernel MLS transformation matrix \( L \).
icell	Cell where each particle is located.
ihoc	Head of chain for each cell (first particle found).
N	Number of particles.
n_cells	Number of cells in each direction
mls_imove	Type of particles affected

Note

The MLS kernel transformation will be computed just for the particles with the moving flag mls_imove, and using just the information of the particles with the moving flag mls_imove

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entry() [16/17]

__kernel void entry	(	const __global int *	imove,
		const __global vec *	r,
		const __global float *	rho,
		const __global float *	m,
		const __global float *	h_var,
		__global float *	shepard,
		usize	N,
		LINKLIST_LOCAL_PARAMS	)

Shepard factor computation.

\[ \gamma(\mathbf{x}) = \int_{\Omega} W(\mathbf{y} - \mathbf{x}) \mathrm{d}\mathbf{x} \]

The shepard renormalization factor is applied for several purposes:

• To interpolate values
• To recover the consistency with the Boundary Integrals formulation
• Debugging

In the shepard factor computation the fluid extension particles are not taken into account.

Parameters

imove	Moving flags. imove > 0 for regular fluid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
r	Position \( \mathbf{r} \).
rho	Density \( \rho \).
m	Mass \( m \).
h_var	variable kernel lenght \( h \).
shepard	Shepard term \( \gamma(\mathbf{x}) = \int_{\Omega} W(\mathbf{y} - \mathbf{x}) \mathrm{d}\mathbf{x} \).
icell	Cell where each particle is located.
ihoc	Head of chain for each cell (first particle found).
N	Number of particles.
n_cells	Number of cells in each direction

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entry() [17/17]

__kernel void entry	(	const __global vec *	normal,
		__global vec *	tangent,
		__global vec *	binormal,
		usize	N )

Compute the tanget vector in 2D simulations, and the binormal vector in 3D simulations.

Parameters

normal	Normal vector \( \mathbf{n} \).
tangent	Tangent vector \( \mathbf{t} \).
binormal	Binormal vector \( \mathbf{t} \).
N	Number of particles.

fields()

__kernel void fields	(	__global const unsigned int *	iset,
		__global const uint *	isplit,
		__global const usize *	mybuffer,
		__global const unsigned int *	ilevel,
		__global const float *	split_weight,
		__global float *	m0,
		__global float *	m,
		__global vec *	r,
		__global vec *	u,
		__global vec *	dudt,
		__global float *	rho,
		__global float *	drhodt,
		__constant float *	dr_level0,
		usize	N,
		LINKLIST_LOCAL_PARAMS	)

Collect the children, and the seed itself, in order to compute the field values of the buffer partner particle.

Since each children may contribute to several partners, we are weighting their field values.

Parameters

isplit	0 if the particle should not become coalesced, 1 for the coalescing particles, 2 for the seeds.
split_weight	Coalescing contribution weight.
m0	Target mass, \( m_0 \).
m	Current mass, \( m \).
r	Position \( \mathbf{r} \).
u	Velocity \( \mathbf{u} \).
dudt	Velocity rate of change \( \frac{d \mathbf{u}}{d t} \).
rho	Density \( \rho \).
drhodt	Density rate of change \( \frac{d \rho}{d t} \).
icell	Cell where each particle is located.
ihoc	Head of chain for each cell (first particle found).
N	Number of particles.
n_cells	Number of cells in each direction

full()

__kernel void full	(	const __global int *	imove,
		const __global vec *	r,
		const __global float *	rho,
		const __global float *	m,
		const __global float *	p,
		__global vec *	lap_p_corr,
		usize	N,
		LINKLIST_LOCAL_PARAMS	)

MLS based correction term.

The term computed with this function should be later renormalized by MLS, using full_mls() function. Before calling such function the user must be sure that both lap_p_corr and mls have been computed (taking into account, for instance, the BCs)

Parameters

imove	Moving flags. imove > 0 for regular fluid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
r	Position \( \mathbf{r} \).
rho	Density \( \rho \).
m	Mass \( m \).
p	Pressure \( p \).
lap_p_corr	Correction term for the Morris Laplacian formula.
icell	Cell where each particle is located.
ihoc	Head of chain for each cell (first particle found).
N	Number of particles.
n_cells	Number of cells in each direction

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full_mls()

__kernel void full_mls	(	const __global int *	imove,
		const __global matrix *	mls,
		__global vec *	lap_p_corr,
		usize	N )

MLS based correction term.

Here the MLS renormalization is applied to the correction term

Parameters

imove	Moving flags. imove > 0 for regular fluid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
r	Position \( \mathbf{r} \).
mls	Kernel MLS transformation matrix \( L \).
lap_p_corr	Correction term for the Morris Laplacian formula.
N	Number of particles.

generate() [1/2]

__kernel void generate	(	__global int *	imove,
		__global int *	iset,
		__global const unsigned int *	isplit,
		__global usize *	split_invperm,
		__global unsigned int *	ilevel,
		__global unsigned int *	level,
		__global int *	miter,
		__global usize *	mybuffer,
		usize	N,
		usize	nbuffer )

Associate a buffer particle to a seed.

Later we are looking for the rest of children, used to compute the variable values of this buffer/partner particle

Parameters

imove	Moving flags. imove > 0 for regular fluid/solid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
iset	Index of the set of particles.
isplit	0 if the particle should not become coalesced, 1 for the coalescing particles, 2 for the seeds.
split_invperm	Permutation to find the index of the particle in the list of particles to become split.
mybuffer	Index of the partner buffer particle.
ilevel	Current refinement level of the particle.
level	Target refinement level of the particle.
miter	Mass transfer iteration (Positive for growing particles, negative for shrinking particles).
mybuffer	Partner particle associated to the seed
N	Number of particles.
nbuffer	Number of available buffer particles.

generate() [2/2]

__kernel void generate	(	__global int *	imove,
		__global int *	iset,
		__global unsigned int *	isplit,
		__global usize *	split_invperm,
		__global unsigned int *	ilevel,
		__global unsigned int *	level,
		__global float *	m0,
		__global int *	miter,
		__global float *	m,
		__global vec *	r,
		__global vec *	u,
		__global vec *	dudt,
		__global float *	rho,
		__global float *	drhodt,
		usize	N,
		usize	nbuffer )

Split a particle in a set of daughter particles.

The daughter particles will be a duplicate of the mother split particle, but conveniently modifying the position and the mass (m0 and gamma_m).

Parameters

imove	Moving flags. imove > 0 for regular fluid/solid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
iset	Index of the set of particles.
isplit	0 if the particle should not become split, 1 otherwise.
split_invperm	Permutation to find the index of the particle in the list of particles to become split.
ilevel	Current refinement level of the particle.
level	Target refinement level of the particle.
m0	Target mass, \( m_0 \).
miter	Mass transfer iteration (Positive for growing particles, negative for shrinking particles).
m	Current mass, \( m \).
r	Position \( \mathbf{r} \).
u	Velocity \( \mathbf{u} \).
dudt	Velocity rate of change \( \frac{d \mathbf{u}}{d t} \).
rho	Density \( \rho \).
drhodt	Density rate of change \( \frac{d \rho}{d t} \).
N	Number of particles.
nbuffer	Number of available buffer particles.

lapp() [1/2]

__kernel void lapp	(	const __global int *	imove,
		const __global vec *	r,
		const __global float *	rho,
		const __global float *	m,
		const __global float *	p,
		__global float *	lap_p,
		usize	N,
		LINKLIST_LOCAL_PARAMS	)

Laplacian of the pressure computation.

Parameters

imove	Moving flags. imove > 0 for regular fluid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
r	Position \( \mathbf{r} \).
rho	Density \( \rho \).
m	Mass \( m \).
p	Pressure \( p \).
lap_p	Pressure laplacian \( \Delta p \).
icell	Cell where each particle is located.
ihoc	Head of chain for each cell (first particle found).
N	Number of particles.
n_cells	Number of cells in each direction

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lapp() [2/2]

__kernel void lapp	(	const __global int *	imove,
		const __global vec *	r,
		const __global float *	rho,
		const __global float *	m,
		const __global float *	p,
		const __global float *	h_var,
		__global float *	lap_p,
		usize	N,
		LINKLIST_LOCAL_PARAMS	)

Laplacian of the pressure computation.

Parameters

imove	Moving flags. imove > 0 for regular fluid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
r	Position \( \mathbf{r} \).
rho	Density \( \rho \).
m	Mass \( m \).
p	Pressure \( p \).
h_var	variable kernel lenght \( h \).
lap_p	Pressure laplacian \( \Delta p \).
icell	Cell where each particle is located.
ihoc	Head of chain for each cell (first particle found).
N	Number of particles.
n_cells	Number of cells in each direction

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lapp_corr()

__kernel void lapp_corr	(	const __global int *	imove,
		const __global vec *	r,
		const __global float *	rho,
		const __global float *	m,
		const __global vec *	lap_p_corr,
		__global float *	lap_p,
		usize	N,
		LINKLIST_LOCAL_PARAMS	)

Laplacian of the pressure correction.

Parameters

imove	Moving flags. imove > 0 for regular fluid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
r	Position \( \mathbf{r} \).
rho	Density \( \rho \).
m	Mass \( m \).
p	Pressure \( p \).
lap_p_corr	Correction term for the Morris Laplacian formula.
lap_p	Pressure laplacian \( \Delta p \).
icell	Cell where each particle is located.
ihoc	Head of chain for each cell (first particle found).
N	Number of particles.
n_cells	Number of cells in each direction

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midpoint()

__kernel void midpoint	(	const __global int *	imove,
		const __global vec *	u_in,
		__global vec *	u,
		const __global vec *	dudt,
		const __global float *	rho_in,
		__global float *	rho,
		const __global float *	drhodt,
		usize	N,
		float	dt )

Advance to the time step midpoint.

Parameters

imove	Moving flags. imove > 0 for regular fluid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
u_in	Velocity \( \mathbf{u}_{n} \).
u	Velocity \( \mathbf{u}_{n+1/2} \).
dudt	Velocity rate of change \( \left. \frac{d \mathbf{u}}{d t} \right\vert_{n+1/2} \).
rho_in	Density \( \rho_{n} \).
rho	Density \( \rho_{n+1/2} \).
drhodt	Density rate of change \( \left. \frac{d \rho}{d t} \right\vert_{n+1/2} \).
N	Number of particles.
dt	Time step \( \Delta t \).

midpoint_r()

__kernel void midpoint_r	(	const __global int *	imove,
		const __global vec *	r_in,
		__global vec *	r,
		const __global vec *	u,
		usize	N,
		float	dt )

Advance the position to the time step midpoint.

Parameters

imove	Moving flags. imove > 0 for regular fluid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
r_in	Position \( \mathbf{r}_{n} \).
r	Position \( \mathbf{r}_{n+1/2} \).
u	Velocity \( \mathbf{u}_{n+1/2} \).
N	Number of particles.
dt	Time step \( \Delta t \).

mls_inv()

__kernel void mls_inv	(	const __global int *	imove,
		__global matrix *	mls,
		usize	N,
		uint	mls_imove )

Invert the matrix computed in entry() to get the final MLS transformation matrix, \( L_i \).

Such transformation matrix can be multiplied by the kernel gradient to produce a new kernel gradient, \( \nabla W^{L}_{ij} = L_i \cdot \nabla W_{ij} \), such that the lienar fields differential operators are consistently computed.

Parameters

imove	Moving flags. imove > 0 for regular fluid/solid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
mls	Kernel MLS transformation matrix \( L \).
N	Number of particles.
mls_imove	Type of particles affected

postcorrector()

__kernel void postcorrector	(	const __global vec *	dudt_as1,
		const __global float *	drhodt_as1,
		const __global vec *	dudt_as2,
		const __global float *	drhodt_as2,
		const __global vec *	dudt_as3,
		const __global float *	drhodt_as3,
		const __global vec *	dudt,
		const __global float *	drhodt,
		__global vec *	dudt_as1_in,
		__global float *	drhodt_as1_in,
		__global vec *	dudt_as2_in,
		__global float *	drhodt_as2_in,
		__global vec *	dudt_as3_in,
		__global float *	drhodt_as3_in,
		__global vec *	dudt_as4_in,
		__global float *	drhodt_as4_in,
		usize	N )

Backup de data for the sorting algorithm.

Parameters

dudt_as1	Velocity rate of change of previous step \( \left. \frac{d \mathbf{u}}{d t} \right\vert_{n-1/2} \).
drhodt_as1	Density rate of change of previous step \( \left. \frac{d \rho}{d t} \right\vert_{n-1/2} \).
dudt_as2	Velocity rate of change of 2 steps ago \( \left. \frac{d \mathbf{u}}{d t} \right\vert_{n-1/2} \).
drhodt_as2	Density rate of change of 2 steps ago \( \left. \frac{d \rho}{d t} \right\vert_{n-1/2} \).
dudt_as3	Velocity rate of change of 3 steps ago \( \left. \frac{d \mathbf{u}}{d t} \right\vert_{n-1/2} \).
drhodt_as3	Density rate of change of 3 steps ago \( \left. \frac{d \rho}{d t} \right\vert_{n-1/2} \).
dudt	Velocity rate of change \( \left. \frac{d \mathbf{u}}{d t} \right\vert_{n+1/2} \).
drhodt	Density rate of change \( \left. \frac{d \rho}{d t} \right\vert_{n+1/2} \).
dudt_as1_in	Velocity rate of change of previous step \( \left. \frac{d \mathbf{u}}{d t} \right\vert_{n-1/2} \).
drhodt_as1_in	Density rate of change of previous step \( \left. \frac{d \rho}{d t} \right\vert_{n-1/2} \).
dudt_as2_in	Velocity rate of change of 2 steps ago \( \left. \frac{d \mathbf{u}}{d t} \right\vert_{n-1/2} \).
drhodt_as2_in	Density rate of change of 2 steps ago \( \left. \frac{d \rho}{d t} \right\vert_{n-1/2} \).
dudt_as3_in	Velocity rate of change of 3 steps ago \( \left. \frac{d \mathbf{u}}{d t} \right\vert_{n-1/2} \).
drhodt_as3_in	Density rate of change of 3 steps ago \( \left. \frac{d \rho}{d t} \right\vert_{n-1/2} \).
dudt_as4_in	Velocity rate of change of 4 steps ago \( \left. \frac{d \mathbf{u}}{d t} \right\vert_{n-1/2} \).
drhodt_as4_in	Density rate of change of 4 steps ago \( \left. \frac{d \rho}{d t} \right\vert_{n-1/2} \).
N	Number of particles.

predictor() [1/3]

__kernel void predictor	(	__global int *	imove,
		__global vec *	r,
		__global vec *	u,
		__global vec *	dudt,
		__global float *	rho,
		__global float *	drhodt,
		__global vec *	r_in,
		__global vec *	u_in,
		__global vec *	dudt_in,
		__global float *	rho_in,
		__global float *	drhodt_in,
		usize	N,
		float	dt )

Improved Euler time integration scheme predictor stage.

Parameters

imove	Moving flags. imove > 0 for regular fluid/solid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
r	Position \( \mathbf{r}_{n+1} \).
u	Velocity \( \mathbf{u}_{n+1} \).
dudt	Velocity rate of change \( \left. \frac{d \mathbf{u}}{d t} \right\vert_{n+1} \).
rho	Density \( \rho_{n+1} \).
drhodt	Density rate of change \( \left. \frac{d \rho}{d t} \right\vert_{n+1} \).
r_in	Position \( \mathbf{r}_{n+1/2} \).
u_in	Velocity \( \mathbf{u}_{n+1/2} \).
dudt_in	Velocity rate of change \( \left. \frac{d \mathbf{u}}{d t} \right\vert_{n+1/2} \).
rho_in	Density \( \rho_{n+1/2} \).
drhodt_in	Density rate of change \( \left. \frac{d \rho}{d t} \right\vert_{n+1/2} \).
N	Number of particles.
dt	Time step \( \Delta t \).

predictor() [2/3]

__kernel void predictor	(	__global vec *	r,
		__global vec *	u,
		__global vec *	dudt,
		__global float *	rho,
		__global float *	drhodt,
		__global vec *	r_in,
		__global vec *	u_in,
		__global vec *	dudt_in,
		__global float *	rho_in,
		__global float *	drhodt_in,
		usize	N )

Adams-Bashforth time integration scheme predictor stage.

1st order Euler time integration scheme predictor stage

Parameters

imove	Moving flags. imove > 0 for regular fluid/solid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
r	Position \( \mathbf{r}_{n+1} \).
u	Velocity \( \mathbf{u}_{n+1} \).
dudt	Velocity rate of change \( \left. \frac{d \mathbf{u}}{d t} \right\vert_{n+1} \).
rho	Density \( \rho_{n+1} \).
drhodt	Density rate of change \( \left. \frac{d \rho}{d t} \right\vert_{n+1} \).
r_in	Position \( \mathbf{r}_{n+1/2} \).
u_in	Velocity \( \mathbf{u}_{n+1/2} \).
dudt_in	Velocity rate of change \( \left. \frac{d \mathbf{u}}{d t} \right\vert_{n+1/2} \).
rho_in	Density \( \rho_{n+1/2} \).
drhodt_in	Density rate of change \( \left. \frac{d \rho}{d t} \right\vert_{n+1/2} \).
N	Number of particles.

predictor() [3/3]

__kernel void predictor	(	const __global vec *	r,
		const __global vec *	u,
		const __global vec *	dudt,
		const __global float *	rho,
		const __global float *	drhodt,
		__global vec *	r_in,
		__global vec *	u_in,
		__global vec *	dudt_in,
		__global float *	rho_in,
		__global float *	drhodt_in,
		usize	N )

Semi-implicit Midpoint Euler time integration scheme predictor stage.

Parameters

imove	Moving flags. imove > 0 for regular fluid/solid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
r	Position \( \mathbf{r}_{n+1} \).
u	Velocity \( \mathbf{u}_{n+1} \).
dudt	Velocity rate of change \( \left. \frac{d \mathbf{u}}{d t} \right\vert_{n+1} \).
rho	Density \( \rho_{n+1} \).
drhodt	Density rate of change \( \left. \frac{d \rho}{d t} \right\vert_{n+1} \).
r_in	Position \( \mathbf{r}_{n+1/2} \).
u_in	Velocity \( \mathbf{u}_{n+1/2} \).
dudt_in	Velocity rate of change \( \left. \frac{d \mathbf{u}}{d t} \right\vert_{n+1/2} \).
rho_in	Density \( \rho_{n+1/2} \).
drhodt_in	Density rate of change \( \left. \frac{d \rho}{d t} \right\vert_{n+1/2} \).
N	Number of particles.

relax()

__kernel void relax	(	const __global int *	imove,
		__global vec *	dudt_in,
		__global vec *	dudt,
		__global float *	drhodt_in,
		__global float *	drhodt,
		usize	N,
		float	relax_midpoint )

residuals()

__kernel void residuals	(	const __global int *	imove,
		const __global float *	m,
		const __global vec *	u,
		const __global vec *	dudt_in,
		const __global vec *	dudt,
		const __global float *	rho,
		const __global float *	p,
		const __global float *	drhodt_in,
		const __global float *	drhodt,
		__global float *	residual_midpoint,
		usize	N )

seed_candidates()

__kernel void seed_candidates	(	__global const unsigned int *	iset,
		__global const int *	imove,
		__global const unsigned int *	ilevel,
		__global const unsigned int *	level,
		__global const float *	m0,
		__global int *	miter,
		__global const vec *	r,
		__global unsigned int *	isplit,
		__global svec *	split_cell,
		__global float *	split_dist,
		__constant float *	dr_level0,
		usize	N )

Look for all the seed candidates, i.e. all the particles which have a refinement level target lower than their current value.

This tool is also placing the particles into cells with the volume of the partner particle to become generated

Parameters

iset	Set of particles index.
imove	Moving flags. imove > 0 for regular fluid/solid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
ilevel	Current refinement level of the particle.
level	Target refinement level of the particle.
m0	Mass \( m_0 \).
miter	Mass transfer iteration (Positive for growing particles, negative for shrinking particles).
r	Position \( \mathbf{r} \).
isplit	0 if the particle should not become coalesced, 1 for the coalescing particles, 2 for the seeds.
split_cell	Seed cell where the particle is located.
split_dist	Distance to the center of the cell. Just the closest particle to the cell center will be kept as seed
dr_level0	Theoretical distance between particles at the lowest refinement level.
N	Number of particles.

seeds()

__kernel void seeds	(	__global const unsigned int *	iset,
		__global const unsigned int *	isplit_in,
		__global unsigned int *	isplit,
		__global int *	miter,
		__global const svec *	split_cell,
		__global const float *	split_dist,
		usize	N,
		LINKLIST_LOCAL_PARAMS	)

Get only one seed per cell.

To do that, all the seed candidates will inspect their neighbours, and in case they find another seed candidate closer to the cell center, they are desisting to become a seed.

Parameters

iset	Set of particles index.
isplit_in	0 if the particle should not become coalesced, 1 for the coalescing particles, 2 for the seeds. This array is used to read.
isplit	0 if the particle should not become coalesced, 1 for the coalescing particles, 2 for the seeds. This array is used to write.
miter	Mass transfer iteration (Positive for growing particles, negative for shrinking particles).
split_cell	Seed cell where the particle is located.
split_dist	Distance to the center of the cell. Just the closest particle to the cell center will be kept as seed
icell	Cell where each particle is located.
ihoc	Head of chain for each cell (first particle found).
N	Number of particles.
n_cells	Number of cells in each direction

set_imove()

__kernel void set_imove	(	__global int *	imove,
		usize	N )

Replace the particles with the imove flag imove=-256 by imove=-255.

The particles with imove=-256 are "invalid particles", i.e. particles which has been removed (e.g. particles out of the computational domain), while imove=-255 are buffer particles.

In that way, the removed particles in a time step are not taken into account as buffer particles until they are sorted at the next time step.

Parameters

imove	Moving flags (imove = -255 for buffer particles).
ibuffer	0 if the particle is not a buffer particle, 1 otherwise.
N	Number of particles.

set_isplit_in()

__kernel void set_isplit_in	(	__global const unsigned int *	isplit,
		__global unsigned int *	isplit_in,
		usize	N )

Create a copy of isplit, where everything is 0 except the seeds, which take the value 1. Such array can be used to count the number of new particles to become generated.

Create a copy of isplit, where the data "out of bounds" is set to 0, instead of 2. Such array can be used to count the number of new particles to become generated.

Parameters

isplit	0 if the particle should not become split, 1 otherwise
isplit_in	0 if the particle should not become split, 1 otherwise
N	Number of particles.

set_mass()

__kernel void set_mass	(	__global const int *	imove,
		__global const float *	m0,
		__global int *	miter,
		__global float *	m,
		usize	N )

Set the mass of the particles according to their gamma value.

When a particle is split in a set of daughter particles, in order to avoid shocks, its effect is smoothly transfered to the daughters, using for that a \( \gamma_m \) mass multiplier.

Parameters

imove	Moving flags. imove > 0 for regular fluid/solid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
m0	Target mass, \( m_0 \). When a particle is split/coalesced, its mass is progressively transfered to its children.
miter	Mass transfer iteration (Positive for growing particles, negative for shrinking particles).
m	Current mass \( m \).
N	Number of particles.

simple()

__kernel void simple	(	const __global unsigned int *	iset,
		const __global int *	imove,
		__global vec *	lap_p_corr,
		__constant float *	refd,
		usize	N,
		vec	g )

Simple hidrostatic based correction term.

Parameters

iset	Set of particles index.
imove	Moving flags. imove = 2 for regular solid particles. imove = 0 for sensors (ignored by this preset). imove < 0 for boundary elements/particles.
lap_p_corr	Correction term for the Morris Laplacian formula.
refd	Density of reference of the fluid \( \rho_0 \).
N	Number of particles.
g	Gravity acceleration \( \mathbf{g} \).

sort()

__kernel void sort	(	const __global vec *	dudt_as1_in,
		__global vec *	dudt_as1,
		const __global vec *	dudt_as2_in,
		__global vec *	dudt_as2,
		const __global vec *	dudt_as3_in,
		__global vec *	dudt_as3,
		const __global vec *	dudt_as4_in,
		__global vec *	dudt_as4,
		const __global float *	drhodt_as1_in,
		__global float *	drhodt_as1,
		const __global float *	drhodt_as2_in,
		__global float *	drhodt_as2,
		const __global float *	drhodt_as3_in,
		__global float *	drhodt_as3,
		const __global float *	drhodt_as4_in,
		__global float *	drhodt_as4,
		const __global usize *	id_sorted,
		usize	N )

Sort the stored Adams-Bashforth stored variation rates.

Parameters

id_in	Unsorted particle indexes
id	Sorted particle indexes
iset_in	Unsorted set of particles indexes.
iset	Sorted set of particles indexes.
imove_in	Unsorted moving flags. imove > 0 for regular fluid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
imove	Sorted moving flags. imove > 0 for regular fluid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
r_in	Unsorted position \( \mathbf{r} \).
r	Sorted position \( \mathbf{r} \).
normal_in	Unsorted normal \( \mathbf{n} \).
normal	Sorted normal \( \mathbf{n} \).
u_in	Unsorted velocity \( \mathbf{u} \).
u	Sorted velocity \( \mathbf{u} \).
id_sorted	Permutations list from the unsorted space to the sorted one.
N	Number of particles.

stage1()

__kernel void stage1	(	const __global usize *	id_in,
		__global usize *	id,
		const __global uint *	iset_in,
		__global uint *	iset,
		const __global int *	imove_in,
		__global int *	imove,
		const __global vec *	r_in,
		__global vec *	r,
		const __global vec *	normal_in,
		__global vec *	normal,
		const __global vec *	tangent_in,
		__global vec *	tangent,
		const __global usize *	id_sorted,
		usize	N )

Sort all the particle variables by the cell indexes.

Due to the large number of registers consumed (21 global memory arrays are loaded), it is safer carrying out the sorting process in to stages. This is the first stage.

Parameters

id_in	Unsorted particle indexes
id	Sorted particle indexes
iset_in	Unsorted set of particles indexes.
iset	Sorted set of particles indexes.
imove_in	Unsorted moving flags. imove > 0 for regular fluid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
imove	Sorted moving flags. imove > 0 for regular fluid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
r_in	Unsorted position \( \mathbf{r} \).
r	Sorted position \( \mathbf{r} \).
normal_in	Unsorted normal \( \mathbf{n} \).
normal	Sorted normal \( \mathbf{n} \).
tangent_in	Unsorted tangent \( \mathbf{t} \).
tangent	Sorted tangent \( \mathbf{t} \).
id_sorted	Permutations list from the unsorted space to the sorted one.
N	Number of particles.

stage2()

__kernel void stage2	(	const __global float *	rho_in,
		__global float *	rho,
		const __global float *	m_in,
		__global float *	m,
		const __global vec *	u_in,
		__global vec *	u,
		const __global vec *	dudt,
		__global vec *	dudt_in,
		const __global float *	drhodt,
		__global float *	drhodt_in,
		const __global usize *	id_sorted,
		usize	N )

Sort all the particle variables by the cell indexes.

Due to the large number of registers consumed (21 global memory arrays are loaded), it is safer carrying out the sorting process in to stages. This is the first stage.

Parameters

rho_in	Unsorted density \( \rho \).
rho	Sorted density \( \rho \).
m_in	Unsorted mass \( m \).
m	Sorted mass \( m \).
u_in	Unsorted velocity \( \mathbf{u} \).
u	Sorted velocity \( \mathbf{u} \).
dudt	Unsorted velocity rate of change \( \frac{d \mathbf{u}}{d t} \).
dudt_in	Sorted velocity rate of change \( \frac{d \mathbf{u}}{d t} \).
drhodt	Unsorted density rate of change \( \frac{d \rho}{d t} \).
drhodt_in	Sorted density rate of change \( \frac{d \rho}{d t} \).
id_sorted	Permutations list from the unsorted space to the sorted one.
N	Number of particles.

weights()

__kernel void weights	(	__global const unsigned int *	iset,
		__global const unsigned int *	ilevel,
		__global const vec *	r,
		__global const unsigned int *	isplit,
		__global float *	split_weight,
		__constant float *	dr_level0,
		usize	N,
		LINKLIST_LOCAL_PARAMS	)

Compute the contribution weight of each children particle.

The children particles (including the seed itself) may be close enough to several partner particles, such that, at the time of computing the partner particles properties, it is eventually contributing to several partners. Hence, the contributions should be conveniently weighted

See also

children()

Parameters

iset	Set of particles index.
ilevel	Current refinement level of the particle.
r	Position \( \mathbf{r} \).
isplit	0 if the particle should not become coalesced, 1 for the coalescing particles, 2 for the seeds.
split_weight	Coalescing contribution weight.
icell	Cell where each particle is located.
ihoc	Head of chain for each cell (first particle found).
dr_level0	Theoretical distance between particles at the lowest refinement level.
N	Number of particles.
n_cells	Number of cells in each direction