void FluidSim::compute_phi() {
//Estimate from particles
liquid_phi.assign(3*dx);
for(unsigned int p = 0; p < particles.size(); ++p) {
Vec2f point = particles[p];
int i,j;
float fx,fy;
//determine containing cell;
get_barycentric((point[0])/dx-0.5f, i, fx, 0, ni);
get_barycentric((point[1])/dx-0.5f, j, fy, 0, nj);
//compute distance to surrounding few points, keep if it's the minimum
for(int j_off = j-2; j_off<=j+2; ++j_off) for(int i_off = i-2; i_off<=i+2; ++i_off) {
if(i_off < 0 || i_off >= ni || j_off < 0 || j_off >= nj)
continue;
Vec2f pos((i_off+0.5f)*dx, (j_off+0.5f)*dx);
float phi_temp = dist(pos, point) - 1.02f*particle_radius;
liquid_phi(i_off,j_off) = min(liquid_phi(i_off,j_off), phi_temp);
}
}
//"extrapolate" phi into solids if nearby
for(int j = 0; j < nj; ++j) {
for(int i = 0; i < ni; ++i) {
if(liquid_phi(i,j) < 0.5*dx) {
float solid_phi_val = 0.25f*(nodal_solid_phi(i,j) + nodal_solid_phi(i+1,j) + nodal_solid_phi(i,j+1) + nodal_solid_phi(i+1,j+1));
if(solid_phi_val < 0)
liquid_phi(i,j) = -0.5f*dx;
}
}
}
}
//Compute finite-volume style face-weights for fluid from nodal signed distances
void FluidSim::compute_weights() {
for(int j = 0; j < u_weights.nj; ++j) for(int i = 0; i < u_weights.ni; ++i) {
u_weights(i,j) = 1 - fraction_inside(nodal_solid_phi(i,j+1), nodal_solid_phi(i,j));
}
for(int j = 0; j < v_weights.nj; ++j) for(int i = 0; i < v_weights.ni; ++i) {
v_weights(i,j) = 1 - fraction_inside(nodal_solid_phi(i+1,j), nodal_solid_phi(i,j));
}
}
//Initialize the grid-based signed distance field that dictates the position of the solid boundary
void FluidSim::set_boundary(float (*phi)(const Vec2f&)) {
for(int j = 0; j < nj+1; ++j) for(int i = 0; i < ni+1; ++i) {
Vec2f pos(i*dx,j*dx);
nodal_solid_phi(i,j) = phi(pos);
}
}
//Initialize the grid-based signed distance field that dictates the position of the solid boundary
void FluidSim::set_boundary(float (*phi)(const Vec3f&)) {
for(int k = 0; k < nk+1; ++k) for(int j = 0; j < nj+1; ++j) for(int i = 0; i < ni+1; ++i) {
Vec3f pos(i*dx,j*dx,k*dx);
nodal_solid_phi(i,j,k) = phi(pos);
}
for(int k = 0; k < nk; ++k) for(int j = 0; j < nj; ++j) for(int i = 0; i < ni; ++i) {
Vec3f pos((i+0.5f)*dx,(j+0.5f)*dx,(k+0.5f)*dx);
cell_solid_phi(i,j,k) = phi(pos);
}
}
void FluidSim::compute_phi() {
//grab from particles
liquid_phi.assign(3*dx);
for(unsigned int p = 0; p < particles.size(); ++p) {
Vec3i cell_ind(particles[p] / dx);
for(int k = max(0,cell_ind[2] - 1); k <= min(cell_ind[2]+1,nk-1); ++k) {
for(int j = max(0,cell_ind[1] - 1); j <= min(cell_ind[1]+1,nj-1); ++j) {
for(int i = max(0,cell_ind[0] - 1); i <= min(cell_ind[0]+1,ni-1); ++i) {
Vec3f sample_pos((i+0.5f)*dx, (j+0.5f)*dx,(k+0.5f)*dx);
float test_val = dist(sample_pos, particles[p]) - particle_radius;
if(test_val < liquid_phi(i,j,k))
liquid_phi(i,j,k) = test_val;
}
}
}
}
//extend phi slightly into solids (this is a simple, naive approach, but works reasonably well)
Array3f phi_temp = liquid_phi;
for(int k = 0; k < nk; ++k) {
for(int j = 0; j < nj; ++j) {
for(int i = 0; i < ni; ++i) {
if(liquid_phi(i,j,k) < 0.5*dx) {
float solid_phi_val = 0.125f*(nodal_solid_phi(i,j,k) + nodal_solid_phi(i+1,j,k) + nodal_solid_phi(i,j+1,k) + nodal_solid_phi(i+1,j+1,k)
+ nodal_solid_phi(i,j,k+1) + nodal_solid_phi(i+1,j,k+1) + nodal_solid_phi(i,j+1,k+1) + nodal_solid_phi(i+1,j+1,k+1));
if(solid_phi_val < 0)
phi_temp(i,j,k) = -0.5f*dx;
}
}
}
}
liquid_phi = phi_temp;
}
//Compute finite-volume style face-weights for fluid from nodal signed distances
void FluidSim::compute_weights() {
//Compute face area fractions (using marching squares cases).
for(int k = 0; k < nk; ++k) for(int j = 0; j < nj; ++j) for(int i = 0; i < ni+1; ++i) {
u_weights(i,j,k) = 1 - fraction_inside(nodal_solid_phi(i,j, k),
nodal_solid_phi(i,j+1,k),
nodal_solid_phi(i,j, k+1),
nodal_solid_phi(i,j+1,k+1));
u_weights(i,j,k) = clamp(u_weights(i,j,k),0.0f,1.0f);
}
for(int k = 0; k < nk; ++k) for(int j = 0; j < nj+1; ++j) for(int i = 0; i < ni; ++i) {
v_weights(i,j,k) = 1 - fraction_inside(nodal_solid_phi(i, j,k),
nodal_solid_phi(i, j,k+1),
nodal_solid_phi(i+1,j,k),
nodal_solid_phi(i+1,j,k+1));
v_weights(i,j,k) = clamp(v_weights(i,j,k),0.0f,1.0f);
}
for(int k = 0; k < nk+1; ++k) for(int j = 0; j < nj; ++j) for(int i = 0; i < ni; ++i) {
w_weights(i,j,k) = 1 - fraction_inside(nodal_solid_phi(i, j, k),
nodal_solid_phi(i, j+1,k),
nodal_solid_phi(i+1,j, k),
nodal_solid_phi(i+1,j+1,k));
w_weights(i,j,k) = clamp(w_weights(i,j,k),0.0f,1.0f);
}
}
void FluidSim::solve_viscosity(float dt) {
int ni = liquid_phi.ni;
int nj = liquid_phi.nj;
//static obstacles for simplicity - for moving objects,
//use a spatially varying 2d array, and modify the linear system appropriately
float u_obj = 0;
float v_obj = 0;
Array2c u_state(ni+1,nj,(const char&)0);
Array2c v_state(ni,nj+1,(const char&)0);
const int SOLID = 1;
const int FLUID = 0;
printf("Determining states\n");
//just determine if the face position is inside the wall! That's it.
for(int j = 0; j < nj; ++j) {
for(int i = 0; i < ni+1; ++i) {
if(i - 1 < 0 || i >= ni || (nodal_solid_phi(i,j+1) + nodal_solid_phi(i,j))/2 <= 0)
u_state(i,j) = SOLID;
else
u_state(i,j) = FLUID;
}
}
for(int j = 0; j < nj+1; ++j) {
for(int i = 0; i < ni; ++i) {
if(j - 1 < 0 || j >= nj || (nodal_solid_phi(i+1,j) + nodal_solid_phi(i,j))/2 <= 0)
v_state(i,j) = SOLID;
else
v_state(i,j) = FLUID;
}
}
printf("Building matrix\n");
int elts = (ni+1)*nj + ni*(nj+1);
if(vrhs.size() != elts) {
vrhs.resize(elts);
velocities.resize(elts);
vmatrix.resize(elts);
}
vmatrix.zero();
float factor = dt/sqr(dx);
for(int j = 1; j < nj-1; ++j) for(int i = 1; i < ni-1; ++i) {
if(u_state(i,j) == FLUID ) {
int index = u_ind(i,j);
vrhs[index] = u_vol(i,j) * u(i,j);
vmatrix.set_element(index,index,u_vol(i,j));
//uxx terms
float visc_right = viscosity(i,j);
float visc_left = viscosity(i-1,j);
float vol_right = c_vol(i,j);
float vol_left = c_vol(i-1,j);
//u_x_right
vmatrix.add_to_element(index,index, 2*factor*visc_right*vol_right);
if(u_state(i+1,j) == FLUID)
vmatrix.add_to_element(index,u_ind(i+1,j), -2*factor*visc_right*vol_right);
else if(u_state(i+1,j) == SOLID)
vrhs[index] -= -2*factor*visc_right*vol_right*u_obj;
//u_x_left
vmatrix.add_to_element(index,index, 2*factor*visc_left*vol_left);
if(u_state(i-1,j) == FLUID)
vmatrix.add_to_element(index,u_ind(i-1,j), -2*factor*visc_left*vol_left);
else if(u_state(i-1,j) == SOLID)
vrhs[index] -= -2*factor*visc_left*vol_left*u_obj;
//uyy terms
float visc_top = 0.25f*(viscosity(i-1,j+1) + viscosity(i-1,j) + viscosity(i,j+1) + viscosity(i,j));
float visc_bottom = 0.25f*(viscosity(i-1,j) + viscosity(i-1,j-1) + viscosity(i,j) + viscosity(i,j-1));
float vol_top = n_vol(i,j+1);
float vol_bottom = n_vol(i,j);
//u_y_top
vmatrix.add_to_element(index,index, +factor*visc_top*vol_top);
if(u_state(i,j+1) == FLUID)
vmatrix.add_to_element(index,u_ind(i,j+1), -factor*visc_top*vol_top);
else if(u_state(i,j+1) == SOLID)
vrhs[index] -= -u_obj*factor*visc_top*vol_top;
//u_y_bottom
vmatrix.add_to_element(index,index, +factor*visc_bottom*vol_bottom);
if(u_state(i,j-1) == FLUID)
vmatrix.add_to_element(index,u_ind(i,j-1), -factor*visc_bottom*vol_bottom);
else if(u_state(i,j-1) == SOLID)
vrhs[index] -= -u_obj*factor*visc_bottom*vol_bottom;
//vxy terms
//v_x_top
if(v_state(i,j+1) == FLUID)
vmatrix.add_to_element(index,v_ind(i,j+1), -factor*visc_top*vol_top);
else if(v_state(i,j+1) == SOLID)
vrhs[index] -= -v_obj*factor*visc_top*vol_top;
if(v_state(i-1,j+1) == FLUID)
vmatrix.add_to_element(index,v_ind(i-1,j+1), factor*visc_top*vol_top);
else if(v_state(i-1,j+1) == SOLID)
vrhs[index] -= v_obj*factor*visc_top*vol_top;
//v_x_bottom
if(v_state(i,j) == FLUID)
vmatrix.add_to_element(index,v_ind(i,j), +factor*visc_bottom*vol_bottom);
else if(v_state(i,j) == SOLID)
vrhs[index] -= v_obj*factor*visc_bottom*vol_bottom;
if(v_state(i-1,j) == FLUID)
vmatrix.add_to_element(index,v_ind(i-1,j), -factor*visc_bottom*vol_bottom);
else if(v_state(i-1,j) == SOLID)
vrhs[index] -= -v_obj*factor*visc_bottom*vol_bottom;
}
}
for(int j = 1; j < nj; ++j) for(int i = 1; i < ni-1; ++i) {
if(v_state(i,j) == FLUID) {
int index = v_ind(i,j);
vrhs[index] = v_vol(i,j)*v(i,j);
vmatrix.set_element(index, index, v_vol(i,j));
//vyy
float visc_top = viscosity(i,j);
float visc_bottom = viscosity(i,j-1);
float vol_top = c_vol(i,j);
float vol_bottom = c_vol(i,j-1);
//vy_top
vmatrix.add_to_element(index,index, +2*factor*visc_top*vol_top);
if(v_state(i,j+1) == FLUID)
vmatrix.add_to_element(index,v_ind(i,j+1), -2*factor*visc_top*vol_top);
else if (v_state(i,j+1) == SOLID)
vrhs[index] -= -2*factor*visc_top*vol_top*v_obj;
//vy_bottom
vmatrix.add_to_element(index,index, +2*factor*visc_bottom*vol_bottom);
if(v_state(i,j-1) == FLUID)
vmatrix.add_to_element(index,v_ind(i,j-1), -2*factor*visc_bottom*vol_bottom);
else if(v_state(i,j-1) == SOLID)
vrhs[index] -= -2*factor*visc_bottom*vol_bottom*v_obj;
//vxx terms
float visc_right = 0.25f*(viscosity(i,j-1) + viscosity(i+1,j-1) + viscosity(i,j) + viscosity(i+1,j));
float visc_left = 0.25f*(viscosity(i,j-1) + viscosity(i-1,j-1) + viscosity(i,j) + viscosity(i-1,j));
float vol_right = n_vol(i+1,j);
float vol_left = n_vol(i,j);
//v_x_right
vmatrix.add_to_element(index,index, +factor*visc_right*vol_right);
if(v_state(i+1,j) == FLUID)
vmatrix.add_to_element(index,v_ind(i+1,j), -factor*visc_right*vol_right);
else if(v_state(i+1,j) == SOLID)
vrhs[index] -= -v_obj*factor*visc_right*vol_right;
//v_x_left
vmatrix.add_to_element(index,index, +factor*visc_left*vol_left);
if(v_state(i-1,j) == FLUID)
vmatrix.add_to_element(index,v_ind(i-1,j), -factor*visc_left*vol_left);
else if(v_state(i-1,j) == SOLID)
vrhs[index] -= -v_obj*factor*visc_left*vol_left;
//uyx
//u_y_right
if(u_state(i+1,j) == FLUID)
vmatrix.add_to_element(index,u_ind(i+1,j), -factor*visc_right*vol_right);
else if(u_state(i+1,j) == SOLID)
vrhs[index] -= -u_obj*factor*visc_right*vol_right;
if(u_state(i+1,j-1) == FLUID)
vmatrix.add_to_element(index,u_ind(i+1,j-1), factor*visc_right*vol_right);
else if(u_state(i+1,j-1) == SOLID)
vrhs[index] -= u_obj*factor*visc_right*vol_right;
//u_y_left
if(u_state(i,j) == FLUID)
vmatrix.add_to_element(index,u_ind(i,j), factor*visc_left*vol_left);
else if(u_state(i,j) == SOLID)
vrhs[index] -= u_obj*factor*visc_left*vol_left;
if(u_state(i,j-1) == FLUID)
vmatrix.add_to_element(index,u_ind(i,j-1), -factor*visc_left*vol_left);
else if(u_state(i,j-1) == SOLID)
vrhs[index] -= -u_obj*factor*visc_left*vol_left;
}
}
double res_out;
int iter_out;
solver.solve(vmatrix, vrhs, velocities, res_out, iter_out);
for(int j = 0; j < nj; ++j)
for(int i = 0; i < ni+1; ++i)
if(u_state(i,j) == FLUID)
u(i,j) = (float)velocities[u_ind(i,j)];
else if(u_state(i,j) == SOLID)
u(i,j) = u_obj;
for(int j = 0; j < nj+1; ++j)
for(int i = 0; i < ni; ++i)
if(v_state(i,j) == FLUID)
v(i,j) = (float)velocities[v_ind(i,j)];
else if(v_state(i,j) == SOLID)
v(i,j) = v_obj;
}
