TimeStep.cl File Reference

Variable time step computation. More...

#include "resources/Scripts/types/types.h"

Include dependency graph for TimeStep.cl:

Functions
__kernel void	entry (const __global int *imove, const __global vec *u, __global float *dt_var, const usize N, const float dt, const float dt_min, const float courant, const float dt_Ma, const float h)
	Compute the maximum time step for each particle.

Detailed Description

Variable time step computation.

Function Documentation

entry()

__kernel void entry	(	const __global int *	imove,
		const __global vec *	u,
		__global float *	dt_var,
		const usize	N,
		const float	dt,
		const float	dt_min,
		const float	courant,
		const float	dt_Ma,
		const float	h )

Compute the maximum time step for each particle.

In SPH the time step is selected to enforce the particles may not move more than \( Ma_{\Delta t} h \), where the Courant factor is not taken into account yet.

Along this line, the distance moved by a particle can be written as follows:

\( \vert \mathbf{r}_{n+1} - \mathbf{r}_{n} \vert = \vert \mathbf{u} \vert \Delta t + \mathcal{O}({\Delta t}^2) \)

Such that rearraging the equation:

\( \Delta t = Ma \frac{h}{\vert \mathbf{u} \vert} \)

Parameters

imove	Moving flags. imove > 0 for regular fluid particles. imove = 0 for sensors. imove < 0 for boundary elements/particles.
u	Velocity \( \mathbf{u}_{n+1/2} \).
dt_var	Variable time step \( \mathrm{min} \left( C_f \frac{h}{c_s}, C_f \frac{h}{10 \vert \mathbf{u} \vert}\right)\).
dt_Ma	The maximum Mach number, \( Ma_{\Delta t} \)
dt	Fixed time step \( \Delta t = C_f \frac{h}{c_s} \).
dt_min	Minimum time step \( \Delta t_{\mathrm{min}} \).
courant	Courant factor \( C_{\Delta t} \).
h	Kernel characteristic length \( h \).
Ma	Mach number \( Ma \).
N	Number of particles.