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Copy pathsolver.cpp
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545 lines (469 loc) · 16.3 KB
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#include "helpers.h"
void
add_source(int N, float * x, float * s, float dt){
int i, size = (N + 2)*(N + 2);
for (i = 0; i < size; i++) x[i] += dt*s[i];
}
void
set_boundaries(int N, int b, float * x){
for (int i = 1; i <= N; i++) {
x[IX(0, i)] = b == 0 ? -x[IX(1, i)] : x[IX(1, i)];
x[IX(N + 1, i)] = b == 0 ? -x[IX(N, i)] : x[IX(N, i)];
x[IX(i, 0)] = b == 0 ? -x[IX(i, 1)] : x[IX(i, 1)];
x[IX(i, N + 1)] = b == -1 ? -x[IX(i, N)] : x[IX(i, N)];
}
x[IX(0, 0)] = 0.5f * (x[IX(1, 0)] + x[IX(0, 1)]);
x[IX(0, N + 1)] = 0.5f * (x[IX(1, N + 1)] + x[IX(0, N)]);
x[IX(N + 1, 0)] = 0.5f * (x[IX(N, 0)] + x[IX(N + 1, 1)]);
x[IX(N + 1, N + 1)] = 0.5f * (x[IX(N, N + 1)] + x[IX(N + 1, N)]);
}
void
Gauss_Seidel_solve(int N, int b, float * x, float * x0, float a, float c, int iterations){
int k;
double h = 1.0f / N;
for (k = 0; k < iterations; k++) {
LOOP_CELLS{
x[IX(i, j)] = (x0[IX(i, j)] + a *
(x[IX(i - 1, j)] + x[IX(i + 1, j)] +
x[IX(i, j - 1)] + x[IX(i, j + 1)])) / c;
}
set_boundaries(N, b, x);
}
}
void
Jacobi_solve(int N, int b, float * x, float * x0, float a, float c, int iterations){
int k;
int size = (N + 2) * (N + 2);
float* aux = (float*)malloc(size*sizeof(float));
double h = 1.0f / (N);
for (k = 0; k < iterations; k++)
{
LOOP_CELLS{
aux[IX(i, j)] = (x0[IX(i, j)] * (h * h) + a *
(x[IX(i - 1, j)] + x[IX(i + 1, j)] +
x[IX(i, j - 1)] + x[IX(i, j + 1)])) / c;
}
LOOP_CELLS{
x[IX(i, j)] = aux[IX(i, j)];
}
set_boundaries(N, b, x);
}
free(aux);
}
void
Multigrid_solve(int N, float * x, float * x0, int nSmooth)
{
}
void
diffuse(int N, int b, float * x, float * x0, float diff, float dt){
float a = dt*diff*N*N;
Gauss_Seidel_solve(N, b, x, x0, a, 1 + 4 * a, 30);
}
vec2
get_velocity(int N, const vec2& position, float * u, float * v){
float u0, v0;
u0 = interpolate(N, position.x * N - 0.0f, position.y * N - 0.5f, u);
v0 = interpolate(N, position.x * N - 0.5f, position.y * N - 0.0f, v);
return vec2(u0, v0);
}
// Mark:
// TODO: Problems make the particles move to wrong direction
// Desc:
// Runge-Kutta 2nd order integration for ODEs
vec2 rk2(int N, float * u, float * v, const vec2& position, float dt){
vec2 vel = get_velocity(N, position, u, v);
vel = get_velocity(N, vec2(position.x + 0.5 * dt * vel.x, position.y + 0.5 * dt * vel.y), u, v);
return vec2(position.x + dt * vel.x, position.y + dt * vel.y);
}
void
particles_advector(int N, float * u, float * v, Particle* particles, int num_particles, float dt){
vec2 pos(0.0f, 0.0f);
for (int i = 0; i != num_particles; i++){
pos.x = pos.y = 0.0f;
pos = rk2(N, u, v, vec2(particles[i].x, particles[i].y), dt);
particles[i].x = pos.x; particles[i].y = pos.y;
particles[i].vel = get_velocity(N, vec2(particles[i].x, particles[i].y), u, v);
}
}
// Problems: Blow up : (
// 2nd order Runge-Kutta ODEs integrator for advection bugs
void
vector_advector_rk2(int N, float * u, float * u0, float * v, float * v0, float * u_tmp, float * v_tmp, float dt){
// TODO: Runge Kutta integrator (2nd order)
}
void
scalar_advector(int N, float * d, float * d0, float * u, float * v, float dt){
int i0, j0, i1, j1;
float x, y, s1, t1, dt0;
dt0 = dt*N;
LOOP_CELLS {
x = i - dt0*u[IX(i, j)];
y = j - dt0*v[IX(i, j)];
if (x < 0.5f) x = 0.5f;
if (x > N + 0.5f) x = N + 0.5f;
i0 = (int)x;
i1 = i0 + 1;
if (y < 0.5f) y = 0.5f;
if (y > N + 0.5f) y = N + 0.5f;
j0 = (int)y;
j1 = j0 + 1;
s1 = x - i0;
t1 = y - j0;
float top_x_dir_lerp = lerp(s1, d0[IX(i0, j0)], d0[IX(i1, j0)]);
float bottom_x_dir_lerp = lerp(s1, d0[IX(i0, j1)], d0[IX(i1, j1)]);
d[IX(i, j)] = lerp(t1, top_x_dir_lerp, bottom_x_dir_lerp);
}
set_boundaries(N, 0, d);
}
void
vector_advector(int N, float * d, float * d0, float * k, float * k0, float * u, float * v, float dt){
int i0, j0, i1, j1;
float x, y, s1, t1, dt0;
// TODO: Modify this piece of code to archive 2nd Order RK
dt0 = dt*N;
LOOP_CELLS {
x = i - dt0*u[IX(i, j)];
y = j - dt0*v[IX(i, j)];
if (x < 0.5f) x = 0.5f;
if (x > N + 0.5f) x = N + 0.5f;
i0 = (int)x;
i1 = i0 + 1;
if (y < 0.5f) y = 0.5f;
if (y > N + 0.5f) y = N + 0.5f;
j0 = (int)y;
j1 = j0 + 1;
s1 = x - i0;
t1 = y - j0;
d[IX(i, j)] = lerp(s1,
lerp(t1, d0[IX(i0, j0)], d0[IX(i0, j1)]),
lerp(t1, d0[IX(i1, j0)], d0[IX(i1, j1)]));
k[IX(i, j)] = lerp(s1,
lerp(t1, k0[IX(i0, j0)], k0[IX(i0, j1)]),
lerp(t1, k0[IX(i1, j0)], k0[IX(i1, j1)]));
}
set_boundaries(N, 0, d);
set_boundaries(N, 0, k);
}
void
project(int N, float * u, float * v, float * p, float * div){
computeDivergence_unifrom(N, u, v, div);
set_boundaries(N, 0, div);
set_boundaries(N, 0, p);
zeros(N, p);
scaler(N, div, -1.0f);
//Multigrid_solve(N, p, div, 10);
Gauss_Seidel_solve(N, 0, p, div, 1, 4, 30);
LOOP_CELLS{
u[IX(i, j)] -= 0.5f*N*(p[IX(i + 1, j)] - p[IX(i - 1, j)]);
v[IX(i, j)] -= 0.5f*N*(p[IX(i, j + 1)] - p[IX(i, j - 1)]);
}
set_boundaries(N, 0, u);
set_boundaries(N, 0, v);
}
void
MoveScalarProperties(int N, float * x, float * x0, float * u, float * v, float diff, float dt){
add_source(N, x, x0, dt);
SWAP(x0, x); diffuse(N, 0, x, x0, diff, dt);
SWAP(x0, x); scalar_advector(N, x, x0, u, v, dt);
}
void SemiLagAdvance(int N,
Particle* particles, int num_particles,
float * fx, float * fy,
float * psi, float * du, float * dv, float * wn, float *dw, float * w_bar, float * w_star,
float * u, float * v, float * u0, float * v0,
float * t, float * t0,
float visc,
float dt){
//// IVOCK advection
zeros(N, wn);
zeros(N, w_bar);
zeros(N, w_star);
zeros(N, dw);
zeros(N, psi);
zeros(N, du);
zeros(N, dv);
zeros(N, u0);
zeros(N, v0);
// Gravity
int size = (N + 2) * (N + 2);
float *g = (float*)malloc(size*sizeof(float));
zeros(N, g);
for (int i = 1; i <= N; i++){
for (int j = 1; j <= N; j++){
g[IX(i, j)] = -9.8;
}
}
add_source(N, u, u0, dt);
add_source(N, v0, g, dt);
add_source(N, v, v0, dt);
particles_advector(N, u, v, particles, num_particles, dt);
SWAP(u0, u);
SWAP(v0, v);
diffuse(N, 0, u, u0, visc, dt);
diffuse(N, 0, v, v0, visc, dt);
project(N, u, v, u0, v0);
zeros(N, u0);
zeros(N, v0);
SWAP(u0, u);
SWAP(v0, v);
computeCurls_uniform(N, wn, u0, v0);
scalar_advector(N, w_bar, wn, u0, v0, dt);
vector_advector(N, u, u0, v, v0, u0, v0, dt);
computeCurls_uniform(N, w_star, u, v);
linear_combine_sub(N, dw, w_bar, w_star);
set_boundaries(N, 0, dw);
scaler(N, dw, -1.0f);
Jacobi_solve(N, 0, psi, dw, 1, 4, 30);
find_vector_potential_2D(N, du, dv, psi);
//linear_combine_add(N, u, u, du);
//linear_combine_add(N, v, v, dv);
free(g);
}
void IVOCKAdvance(int N,
Particle* particles, int num_particles,
float * fx, float * fy,
float * psi, float * du, float * dv, float * wn, float *dw, float * w_bar, float * w_star,
float * u, float * v, float * u0, float * v0,
float * t, float * t0,
float visc,
float dt){
// Only for debug
//// IVOCK advection
zeros(N, wn);
zeros(N, w_bar);
zeros(N, w_star);
zeros(N, dw);
zeros(N, psi);
zeros(N, du);
zeros(N, dv);
zeros(N, u0);
zeros(N, v0);
// Gravity
int size = (N + 2) * (N + 2);
float *g = (float*)malloc(size*sizeof(float));
zeros(N, g);
for (int i = 1; i <= N; i++){
for (int j = 1; j <= N; j++){
g[IX(i, j)] = -9.8;
}
}
add_source(N, u, u0, dt);
add_source(N, v0, g, dt);
add_source(N, v, v0, dt);
particles_advector(N, u, v, particles, num_particles, dt);
SWAP(u0, u);
SWAP(v0, v);
diffuse(N, 0, u, u0, visc, dt);
diffuse(N, 0, v, v0, visc, dt);
project(N, u, v, u0, v0);
zeros(N, u0);
zeros(N, v0);
SWAP(u0, u);
SWAP(v0, v);
computeCurls_uniform(N, wn, u0, v0);
scalar_advector(N, w_bar, wn, u0, v0, dt);
vector_advector(N, u, u0, v, v0, u0, v0, dt);
computeCurls_uniform(N, w_star, u, v);
linear_combine_sub(N, dw, w_bar, w_star);
set_boundaries(N, 0, dw);
scaler(N, dw, -1.0f);
Jacobi_solve(N, 0, psi, dw, 1, 4, 30);
find_vector_potential_2D(N, du, dv, psi);
linear_combine_add(N, u, u, du);
linear_combine_add(N, v, v, dv);
free(g);
}
void add_gravity(int N, float dt, float grav, float * field){
// Gravity
int size = (N + 2) * (N + 2);
float *g = (float*)malloc(size*sizeof(float));
zeros(N, g);
for (int i = 1; i <= N; i++){
for (int j = 1; j <= N; j++){
g[IX(i, j)] = grav;
}
}
add_source(N, field, g, dt);
if (g) free(g);
}
void stream(float * f1, float * f2, float * f3, float * f4,
float * f5, float * f6, float * f7, float * f8,
int N){
int size = (N + 2) * (N + 2);
float * tmpf1 = (float*)malloc(size * sizeof(float));
float * tmpf2 = (float*)malloc(size * sizeof(float));
float * tmpf3 = (float*)malloc(size * sizeof(float));
float * tmpf4 = (float*)malloc(size * sizeof(float));
float * tmpf5 = (float*)malloc(size * sizeof(float));
float * tmpf6 = (float*)malloc(size * sizeof(float));
float * tmpf7 = (float*)malloc(size * sizeof(float));
float * tmpf8 = (float*)malloc(size * sizeof(float));
LOOP_CELLS{
tmpf1[IX(i, j)] = f1[IX(i - 1, j)];
tmpf2[IX(i, j)] = f2[IX(i, j + 1)];
tmpf3[IX(i, j)] = f3[IX(i + 1, j)];
tmpf4[IX(i, j)] = f4[IX(i, j - 1)];
tmpf5[IX(i, j)] = f5[IX(i - 1, j + 1)];
tmpf6[IX(i, j)] = f6[IX(i + 1, j + 1)];
tmpf7[IX(i, j)] = f7[IX(i + 1, j - 1)];
tmpf8[IX(i, j)] = f8[IX(i - 1, j - 1)];
}
LOOP_CELLS{
f1[IX(i, j)] = tmpf1[IX(i, j)];
f2[IX(i, j)] = tmpf2[IX(i, j)];
f3[IX(i, j)] = tmpf3[IX(i, j)];
f4[IX(i, j)] = tmpf4[IX(i, j)];
f5[IX(i, j)] = tmpf5[IX(i, j)];
f6[IX(i, j)] = tmpf6[IX(i, j)];
f7[IX(i, j)] = tmpf7[IX(i, j)];
f8[IX(i, j)] = tmpf8[IX(i, j)];
}
if (tmpf1) free(tmpf1);
if (tmpf2) free(tmpf2);
if (tmpf3) free(tmpf3);
if (tmpf4) free(tmpf4);
if (tmpf5) free(tmpf5);
if (tmpf6) free(tmpf6);
if (tmpf7) free(tmpf7);
if (tmpf8) free(tmpf8);
}
void collision(float * f0,
float * f1, float * f2, float * f3, float * f4,
float * f5, float * f6, float * f7, float * f8,
int N, float tau, float * out_u, float * out_v, float dt){
assert(out_u != NULL && out_v != NULL);
float rho, rho_u, rho_v, _u, _v;
float eq0, eq1, eq2, eq3, eq4, eq5, eq6, eq7, eq8;
float h = 1.f / N;
float c = h / dt;
float c2 = pow(c, 2);
LOOP_CELLS{
rho = f0[IX(i, j)] +
f1[IX(i, j)] + f2[IX(i, j)] + f3[IX(i, j)] + f4[IX(i, j)] +
f5[IX(i, j)] + f6[IX(i, j)] + f7[IX(i, j)] + f8[IX(i, j)];
rho_u = (f1[IX(i, j)] - f3[IX(i, j)] + f5[IX(i, j)] - f6[IX(i, j)] - f7[IX(i, j)] + f8[IX(i, j)]);
rho_v = (f2[IX(i, j)] - f4[IX(i, j)] + f5[IX(i, j)] + f6[IX(i, j)] - f7[IX(i, j)] - f8[IX(i, j)]);
_u = rho_u / rho;
_v = rho_v / rho;
out_u[IX(i, j)] = _u;
out_v[IX(i, j)] = _v;
float coef_vel = 1.5 * (pow(_u, 2) + pow(_v, 2));
eq0 = rho * (4.f / 9.f) * (1.f - coef_vel);
eq1 = rho * (1.f / 9.f) * (1.f + (3.f * _u) + (4.5f * pow(_u, 2)) - coef_vel);
eq2 = rho * (1.f / 9.f) * (1.f + (3.f * _v) + (4.5f * pow(_v, 2)) - coef_vel);
eq3 = rho * (1.f / 9.f) * (1.f - (3.f * _u) + (4.5f * pow(_u, 2)) - coef_vel);
eq4 = rho * (1.f / 9.f) * (1.f - (3.f * _v) + (4.5f * pow(_v, 2)) - coef_vel);
eq5 = rho * (1.f / 36.f) * (1.f + 3.f * ( _u + _v) + 4.5f * pow( _u + _v, 2) - coef_vel);
eq6 = rho * (1.f / 36.f) * (1.f + 3.f * (-_u + _v) + 4.5f * pow(-_u + _v, 2) - coef_vel);
eq7 = rho * (1.f / 36.f) * (1.f + 3.f * (-_u - _v) + 4.5f * pow(-_u - _v, 2) - coef_vel);
eq8 = rho * (1.f / 36.f) * (1.f + 3.f * ( _u - _v) + 4.5f * pow( _u - _v, 2) - coef_vel);
f0[IX(i, j)] = (1.0f - 1.f / tau) * f0[IX(i, j)] + (1.f / tau) * eq0;
f1[IX(i, j)] = (1.0f - 1.f / tau) * f1[IX(i, j)] + (1.f / tau) * eq1;
f2[IX(i, j)] = (1.0f - 1.f / tau) * f2[IX(i, j)] + (1.f / tau) * eq2;
f3[IX(i, j)] = (1.0f - 1.f / tau) * f3[IX(i, j)] + (1.f / tau) * eq3;
f4[IX(i, j)] = (1.0f - 1.f / tau) * f4[IX(i, j)] + (1.f / tau) * eq4;
f5[IX(i, j)] = (1.0f - 1.f / tau) * f5[IX(i, j)] + (1.f / tau) * eq5;
f6[IX(i, j)] = (1.0f - 1.f / tau) * f6[IX(i, j)] + (1.f / tau) * eq6;
f7[IX(i, j)] = (1.0f - 1.f / tau) * f7[IX(i, j)] + (1.f / tau) * eq7;
f8[IX(i, j)] = (1.0f - 1.f / tau) * f8[IX(i, j)] + (1.f / tau) * eq8;
}
}
void bounce_back_BC_LBM(float * f0,
float * f1, float * f2, float * f3, float * f4,
float * f5, float * f6, float * f7, float * f8,
int N, int * solid_mask){
assert(solid_mask != NULL);
float f1_prev, f2_prev, f3_prev, f4_prev, f5_prev, f6_prev, f7_prev, f8_prev;
for (int i = 1; i <= N; i++){
for (int j = 1; j <= N; j++){
if (0 == solid_mask[IX(i, j)]){
f1_prev = f1[IX(i, j)];
f2_prev = f2[IX(i, j)];
f3_prev = f3[IX(i, j)];
f4_prev = f4[IX(i, j)];
f5_prev = f5[IX(i, j)];
f6_prev = f6[IX(i, j)];
f7_prev = f7[IX(i, j)];
f8_prev = f8[IX(i, j)];
f1[IX(i, j)] = f3_prev;
f2[IX(i, j)] = f4_prev;
f3[IX(i, j)] = f1_prev;
f4[IX(i, j)] = f2_prev;
f5[IX(i, j)] = f7_prev;
f6[IX(i, j)] = f8_prev;
f7[IX(i, j)] = f5_prev;
f8[IX(i, j)] = f6_prev;
}
}
}
}
void open_boundary_LBM(float * f0,
float * f1, float * f2, float * f3, float * f4,
float * f5, float * f6, float * f7, float * f8,
int N){
//TODO: Process when fluid leave the domain
}
// Keep adding source.
// This was set to default by keeping source in vertical direction.
void init_state_LBM(float * f2, float * f5, float * f6, int N, int src_range, float init_mag_vel, float rho, float dt){
float h = 1.f / N;
float c = h / dt;
float c2 = pow(c, 2);
int emit_idx = IX(N / 2, 10);
for (int i = N / 2 - src_range; i < N / 2 + src_range; i++){
f2[emit_idx] = rho * 1.f / 9.f * (1.0f + 3.0f * init_mag_vel + 4.5f * pow(init_mag_vel, 2));
f5[emit_idx] = rho * 1.f / 36.f * (1.0f + 3.0f * init_mag_vel + 4.5f * pow(init_mag_vel, 2));
f6[emit_idx] = rho * 1.f / 36.f * (1.0f + 3.0f * init_mag_vel + 4.5f * pow(init_mag_vel, 2));
}
}
void LBMAdvance(float * f0,
float * f1, float * f2, float * f3, float * f4,
float * f5, float * f6, float * f7, float * f8,
int N, float tau, float * out_u, float * out_v,
Particle* particles, int num_particles, float dt){
//particles_advector(N, out_u, out_v, particles, num_particles, dt);
stream(f1, f2, f3, f4, f5, f6, f7, f8, N);
init_state_LBM(f4, f7, f8, N, 2, 0.04f, 1.0f, 1.0);
collision(f0, f1, f2, f3, f4, f5, f6, f7, f8, N, tau, out_u, out_v, dt);
}
// Poisson Equation Laplace(Psi) = f(x);
// Ex.1
// 5x5 with interior field 3x3 and outter boundaries
/*
A =
-4 1 0 1 0 0 0 0 0
1 -4 1 0 1 0 0 0 0
0 1 -4 0 0 1 0 0 0
1 0 0 -4 1 0 1 0 0
0 1 0 1 -4 1 0 1 0
0 0 1 0 1 -4 0 0 1
0 0 0 1 0 0 -4 1 0
0 0 0 0 1 0 1 -4 1
0 0 0 0 0 1 0 1 -4
b' = 5 0 0 0 6 0 0 0 0
10 Times Gauss Seidel solution is:
Step 1 Step 2 Step 3 Step 4 Step 5
-1.25000000000000 -1.40625000000000 -1.64257812500000 -1.75708007812500 -1.81387329101563
-0.312500000000000 -0.785156250000000 -1.01416015625000 -1.12774658203125 -1.18442535400391
-0.0781250000000000 -0.304687500000000 -0.417968750000000 -0.474609375000000 -0.502929687500000
-0.312500000000000 -0.785156250000000 -1.01416015625000 -1.12774658203125 -1.18442535400391
-1.65625000000000 -2.10937500000000 -2.33593750000000 -2.44921875000000 -2.50585937500000
-0.433593750000000 -0.657714843750000 -0.770690917968750 -0.827293395996094 -0.855608940124512
-0.0781250000000000 -0.304687500000000 -0.417968750000000 -0.474609375000000 -0.502929687500000
-0.433593750000000 -0.657714843750000 -0.770690917968750 -0.827293395996094 -0.855608940124512
-0.216796875000000 -0.328857421875000 -0.385345458984375 -0.413646697998047 -0.427804470062256
The exact solution for this system is:
(-1.8705 -1.2411 -0.5313 -1.2411 -2.5625 -0.8839 -0.5313 -0.8839 -0.4420)
Step 6 Step 7 Step 8 Step 9 Step 10
-1.84221267700195 -1.85637521743774 -1.86345559358597 -1.86699566990137 -1.86876569408923
-1.21275043487549 -1.22691118717194 -1.23399133980274 -1.23753138817847 -1.23930140887387
-0.517089843750000 -0.524169921875000 -0.527709960937500 -0.529479980468750 -0.530364990234375
-1.21275043487549 -1.22691118717194 -1.23399133980274 -1.23753138817847 -1.23930140887387
-2.53417968750000 -2.54833984375000 -2.55541992187500 -2.55895996093750 -2.56072998046875
-0.869768500328064 -0.876848503947258 -0.880388533696532 -0.882158552063629 -0.883043561683735
-0.517089843750000 -0.524169921875000 -0.527709960937500 -0.529479980468750 -0.530364990234375
-0.869768500328064 -0.876848503947258 -0.880388533696532 -0.882158552063629 -0.883043561683735
-0.434884250164032 -0.438424251973629 -0.440194266848266 -0.441079276031815 -0.441521780841867
The exact solution for this system is:
(-1.8705 -1.2411 -0.5313 -1.2411 -2.5625 -0.8839 -0.5313 -0.8839 -0.4420)
*/