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d2q9_bgk.c
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#include "d2q9_bgk.h"
#include "immintrin.h"
#include "types.h"
#include <omp.h>
#include <xmmintrin.h>
/* The main processes in one step */
int collision(const t_param params, t_speed *cells, t_speed *tmp_cells,
int *obstacles);
int streaming(const t_param params, t_speed *cells, t_speed *tmp_cells);
int obstacle(const t_param params, t_speed *cells, t_speed *tmp_cells,
int *obstacles);
int boundary(const t_param params, t_speed *cells, t_speed *tmp_cells,
float *inlets);
/*
** The main calculation methods.
** timestep calls, in order, the functions:
** collision(), obstacle(), streaming() & boundary()
*/
int timestep(const t_param params, t_speed *cells, t_speed *tmp_cells,
float *inlets, int *obstacles) {
/* The main time overhead, you should mainly optimize these processes. */
collision(params, cells, tmp_cells, obstacles);
// obstacle(params, cells, tmp_cells, obstacles);
streaming(params, cells, tmp_cells);
boundary(params, cells, tmp_cells, inlets);
return EXIT_SUCCESS;
}
/*
** The collision of fluids in the cell is calculated using
** the local equilibrium distribution and relaxation process
*/
int collision(const t_param params, t_speed *cells, t_speed *tmp_cells,
int *obstacles) {
const float c_sq = 1.f / 3.f; /* square of speed of sound */
const float w0 = 4.f / 9.f; /* weighting factor */
const float w1 = 1.f / 9.f; /* weighting factor */
const float w2 = 1.f / 36.f; /* weighting factor */
/* loop over the cells in the grid
** the collision step is called before
** the streaming step and so values of interest
** are in the scratch-space grid */
__m256 _1 = _mm256_set1_ps(1.f);
__m256 c = _mm256_set1_ps(c_sq);
__m256 _2_c_c = _mm256_set1_ps(2.f * c_sq * c_sq);
__m256 w = _mm256_setr_ps(w1, w1, w1, w1, w2, w2, w2, w2);
__m256 omega = _mm256_set1_ps(params.omega);
#pragma omp parallel for
for (int jj = 0; jj < params.ny; jj++) {
float buffer[8];
for (int ii = 0; ii < params.nx; ii++) {
if (!obstacles[ii + jj * params.nx]) {
/* compute local density total */
float local_density = 0.f;
for (int kk = 0; kk < NSPEEDS; kk++) {
local_density += cells->speeds[kk][ii + jj * params.nx];
}
/* compute x velocity component */
float u_x = (cells->speeds[1][ii + jj * params.nx] +
cells->speeds[5][ii + jj * params.nx] +
cells->speeds[8][ii + jj * params.nx] -
(cells->speeds[3][ii + jj * params.nx] +
cells->speeds[6][ii + jj * params.nx] +
cells->speeds[7][ii + jj * params.nx])) /
local_density;
/* compute y velocity component */
float u_y = (cells->speeds[2][ii + jj * params.nx] +
cells->speeds[5][ii + jj * params.nx] +
cells->speeds[6][ii + jj * params.nx] -
(cells->speeds[4][ii + jj * params.nx] +
cells->speeds[7][ii + jj * params.nx] +
cells->speeds[8][ii + jj * params.nx])) /
local_density;
/* velocity squared */
float u_sq = u_x * u_x + u_y * u_y;
/* equilibrium densities */
float d_equ;
/* zero velocity density: weight w0 */
d_equ = w0 * local_density * (1.f - u_sq / (2.f * c_sq));
__m256 x = _mm256_setr_ps(u_x, u_y, -u_x, -u_y, u_x + u_y, -u_x + u_y,
-u_x - u_y, u_x - u_y);
__m256 res = _mm256_add_ps(
_mm256_add_ps(_1, _mm256_div_ps(x, c)),
_mm256_sub_ps(_mm256_div_ps(_mm256_mul_ps(x, x), _2_c_c),
_mm256_set1_ps(u_sq / (2.f * c_sq))));
res =
_mm256_mul_ps(_mm256_mul_ps(res, _mm256_set1_ps(local_density)), w);
/* relaxation step */
tmp_cells->speeds[0][ii + jj * params.nx] =
cells->speeds[0][ii + jj * params.nx] +
params.omega * (d_equ - cells->speeds[0][ii + jj * params.nx]);
__m256 c_s = _mm256_setr_ps(cells->speeds[1][ii + jj * params.nx],
cells->speeds[2][ii + jj * params.nx],
cells->speeds[3][ii + jj * params.nx],
cells->speeds[4][ii + jj * params.nx],
cells->speeds[5][ii + jj * params.nx],
cells->speeds[6][ii + jj * params.nx],
cells->speeds[7][ii + jj * params.nx],
cells->speeds[8][ii + jj * params.nx]);
// __m256 c_s = _mm256_loadu_ps(cells[ii + jj * params.nx].speeds +
// 1);
res = _mm256_add_ps(_mm256_mul_ps(_mm256_sub_ps(res, c_s), omega), c_s);
_mm256_storeu_ps(buffer, res);
for (int k = 1; k < NSPEEDS; ++k)
tmp_cells->speeds[k][ii + jj * params.nx] = buffer[k - 1];
} else {
tmp_cells->speeds[0][ii + jj * params.nx] =
cells->speeds[0][ii + jj * params.nx];
tmp_cells->speeds[1][ii + jj * params.nx] =
cells->speeds[3][ii + jj * params.nx];
tmp_cells->speeds[3][ii + jj * params.nx] =
cells->speeds[1][ii + jj * params.nx];
tmp_cells->speeds[2][ii + jj * params.nx] =
cells->speeds[4][ii + jj * params.nx];
tmp_cells->speeds[4][ii + jj * params.nx] =
cells->speeds[2][ii + jj * params.nx];
tmp_cells->speeds[5][ii + jj * params.nx] =
cells->speeds[7][ii + jj * params.nx];
tmp_cells->speeds[7][ii + jj * params.nx] =
cells->speeds[5][ii + jj * params.nx];
tmp_cells->speeds[6][ii + jj * params.nx] =
cells->speeds[8][ii + jj * params.nx];
tmp_cells->speeds[8][ii + jj * params.nx] =
cells->speeds[6][ii + jj * params.nx];
}
}
}
return EXIT_SUCCESS;
}
/*
** For obstacles, mirror their speed.
*/
int obstacle(const t_param params, t_speed *cells, t_speed *tmp_cells,
int *obstacles) {
/* loop over the cells in the grid */
#pragma omp parallel for
for (int jj = 0; jj < params.ny; jj++) {
for (int ii = 0; ii < params.nx; ii++) {
/* if the cell contains an obstacle */
if (obstacles[jj * params.nx + ii]) {
/* called after collision, so taking values from scratch space
** mirroring, and writing into main grid */
tmp_cells->speeds[0][ii + jj * params.nx] =
cells->speeds[0][ii + jj * params.nx];
tmp_cells->speeds[1][ii + jj * params.nx] =
cells->speeds[3][ii + jj * params.nx];
tmp_cells->speeds[3][ii + jj * params.nx] =
cells->speeds[1][ii + jj * params.nx];
tmp_cells->speeds[2][ii + jj * params.nx] =
cells->speeds[4][ii + jj * params.nx];
tmp_cells->speeds[4][ii + jj * params.nx] =
cells->speeds[2][ii + jj * params.nx];
tmp_cells->speeds[5][ii + jj * params.nx] =
cells->speeds[7][ii + jj * params.nx];
tmp_cells->speeds[7][ii + jj * params.nx] =
cells->speeds[5][ii + jj * params.nx];
tmp_cells->speeds[6][ii + jj * params.nx] =
cells->speeds[8][ii + jj * params.nx];
tmp_cells->speeds[8][ii + jj * params.nx] =
cells->speeds[6][ii + jj * params.nx];
}
}
}
return EXIT_SUCCESS;
}
/*
** Particles flow to the corresponding cell according to their speed direaction.
*/
int streaming(const t_param params, t_speed *cells, t_speed *tmp_cells) {
/* loop over _all_ cells */
#pragma omp parallel for
for (int jj = 0; jj < params.ny; jj++) {
for (int ii = 0; ii < params.nx; ii++) {
/* determine indices of axis-direction neighbours
** respecting periodic boundary conditions (wrap around) */
int y_n = (jj + 1) % params.ny;
int x_e = (ii + 1) % params.nx;
int y_s = (jj == 0) ? (params.ny - 1) : (jj - 1);
int x_w = (ii == 0) ? (params.nx - 1) : (ii - 1);
/* propagate densities from neighbouring cells, following
** appropriate directions of travel and writing into
** scratch space grid */
cells->speeds[0][ii + jj * params.nx] =
tmp_cells
->speeds[0][ii + jj * params.nx]; /* central cell, no movement */
cells->speeds[1][x_e + jj * params.nx] =
tmp_cells->speeds[1][ii + jj * params.nx]; /* east */
cells->speeds[2][ii + y_n * params.nx] =
tmp_cells->speeds[2][ii + jj * params.nx]; /* north */
cells->speeds[3][x_w + jj * params.nx] =
tmp_cells->speeds[3][ii + jj * params.nx]; /* west */
cells->speeds[4][ii + y_s * params.nx] =
tmp_cells->speeds[4][ii + jj * params.nx]; /* south */
cells->speeds[5][x_e + y_n * params.nx] =
tmp_cells->speeds[5][ii + jj * params.nx]; /* north-east */
cells->speeds[6][x_w + y_n * params.nx] =
tmp_cells->speeds[6][ii + jj * params.nx]; /* north-west */
cells->speeds[7][x_w + y_s * params.nx] =
tmp_cells->speeds[7][ii + jj * params.nx]; /* south-west */
cells->speeds[8][x_e + y_s * params.nx] =
tmp_cells->speeds[8][ii + jj * params.nx]; /* south-east */
}
}
return EXIT_SUCCESS;
}
/*
** Work with boundary conditions. The upper and lower boundaries use the rebound
*plane,
** the left border is the inlet of fixed speed, and
** the right border is the open outlet of the first-order approximation.
*/
int boundary(const t_param params, t_speed *cells, t_speed *tmp_cells,
float *inlets) {
/* Set the constant coefficient */
const float cst1 = 2.0 / 3.0;
const float cst2 = 1.0 / 6.0;
const float cst3 = 1.0 / 2.0;
int ii, jj;
float local_density;
// top wall (bounce)
jj = params.ny - 1;
#pragma omp parallel for
for (ii = 0; ii < params.nx; ii++) {
cells->speeds[4][ii + jj * params.nx] =
tmp_cells->speeds[2][ii + jj * params.nx];
cells->speeds[7][ii + jj * params.nx] =
tmp_cells->speeds[5][ii + jj * params.nx];
cells->speeds[8][ii + jj * params.nx] =
tmp_cells->speeds[6][ii + jj * params.nx];
}
// bottom wall (bounce)
jj = 0;
#pragma omp parallel for
for (ii = 0; ii < params.nx; ii++) {
cells->speeds[2][ii + jj * params.nx] =
tmp_cells->speeds[4][ii + jj * params.nx];
cells->speeds[5][ii + jj * params.nx] =
tmp_cells->speeds[7][ii + jj * params.nx];
cells->speeds[6][ii + jj * params.nx] =
tmp_cells->speeds[8][ii + jj * params.nx];
}
// left wall (inlet)
ii = 0;
#pragma omp parallel for
for (jj = 0; jj < params.ny; jj++) {
local_density = (cells->speeds[0][ii + jj * params.nx] +
cells->speeds[2][ii + jj * params.nx] +
cells->speeds[4][ii + jj * params.nx] +
2.0 * cells->speeds[3][ii + jj * params.nx] +
2.0 * cells->speeds[6][ii + jj * params.nx] +
2.0 * cells->speeds[7][ii + jj * params.nx]) /
(1.0 - inlets[jj]);
cells->speeds[1][ii + jj * params.nx] =
cells->speeds[3][ii + jj * params.nx] +
cst1 * local_density * inlets[jj];
cells->speeds[5][ii + jj * params.nx] =
cells->speeds[7][ii + jj * params.nx] -
cst3 * (cells->speeds[2][ii + jj * params.nx] -
cells->speeds[4][ii + jj * params.nx]) +
cst2 * local_density * inlets[jj];
cells->speeds[8][ii + jj * params.nx] =
cells->speeds[6][ii + jj * params.nx] +
cst3 * (cells->speeds[2][ii + jj * params.nx] -
cells->speeds[4][ii + jj * params.nx]) +
cst2 * local_density * inlets[jj];
}
// right wall (outlet)
ii = params.nx - 1;
#pragma omp parallel for
for (jj = 0; jj < params.ny; jj++) {
for (int kk = 0; kk < NSPEEDS; kk++) {
cells->speeds[kk][ii + jj * params.nx] =
cells->speeds[kk][ii - 1 + jj * params.nx];
}
}
return EXIT_SUCCESS;
}