Variable time step computation. More...

#include "resources/Scripts/types/types.h"
#include "resources/Scripts/KernelFunctions/Kernel.h"
#include "resources/Scripts/cfd/ideal_gas/sound_speed.hcl"

Include dependency graph for TimeStep.cl:

Functions
__kernel void	entry (__global float dt_var, const __global int imove, const __global unsigned int iset, const __global vec u, const __global vec dudt, const __global float rho, const __global float p, const __global float m, const usize N, const float dt, const float dt_min, const float courant, const float h, const __global float div_u, const __global vec grad_p, __constant float *gamma)
	Compute the maximum time step for each particle.

Detailed Description

Variable time step computation.

Function Documentation

◆ entry()

__kernel void entry	(	__global float *	dt_var,
		const __global int *	imove,
		const __global unsigned int *	iset,
		const __global vec *	u,
		const __global vec *	dudt,
		const __global float *	rho,
		const __global float *	p,
		const __global float *	m,
		const usize	N,
		const float	dt,
		const float	dt_min,
		const float	courant,
		const float	h,
		const __global float *	div_u,
		const __global vec *	grad_p,
		__constant float *	gamma )

Compute the maximum time step for each particle.

In SPH the time step is selected to enforce the particles may not move more than \( 0.1 h \), where the Courant factor is not taken into account yet.

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

\( \vert \mathbf{r}_{n+1} - \mathbf{r}_{n} \vert = \vert \mathbf{u} \vert \Delta t + \frac{1}{2} \left\vert \frac{\mathrm{d} \mathbf{u}}{\mathrm{d} t} \right\vert {\Delta t}^2 + \mathcal{O}({\Delta t}^3) \)

Such that, taking maximums, and rearraging the equation:

\( \Delta t = \frac{1}{20} \min \left( \frac{h}{\vert \mathbf{u} \vert}, \sqrt{\frac{2 h}{\left\vert \frac{\mathrm{d} \mathbf{u}}{\mathrm{d} t} \right\vert}} \right) \)

Parameters

dt_var	Variable time step \( \mathrm{min} \left( C_f \frac{h}{c_s}, C_f \frac{h}{10 \vert \mathbf{u} \vert}\right)\).
u	Velocity \( \mathbf{u}_{n+1/2} \).
dudt	Velocity rate of change \( \frac{d \mathbf{u}}{d t} \).
N	Number of particles.
dt	Fixed time step \( \Delta t = C_f \frac{h}{c_s} \).
dt_min	Minimum time step \( \Delta t_{\mathrm{min}} \).
courant	Courant factor \( C_f \).
h	Kernel characteristic length \( h \).

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