Suggestion on bufferzone to reduce acoustic reflection on TYPE_E boundaries

I noticed period oscillations from acoustic waves reflecting on the TYPE_E boundaries. I've added a buffer zone to these boundaries to help reduce the reflection.

The buffer zone code is a first version. Please adjust the parameters as needed.

In LBM code. Add:

R(float compute_type_e_blend_factor_simple(const uint3 xyz) {
//const int dist_x = min((int)xyz.x, (int)def_Nx - 1 - (int)xyz.x);
const int dist_y = min((int)xyz.y, (int)def_Ny - 1 - (int)xyz.y);
const int dist_z = min((int)xyz.z, (int)def_Nz - 1 - (int)xyz.z);
const int min_dist = min(dist_y, dist_z);

// Bufferzone size=10!!!  Defined by your self
const int BLEND_RANGE = 10;

if(min_dist > BLEND_RANGE) {
    return 1.0f;  // }

// alpha = (dist/10)^3
const float normalized = (float)min_dist / (float)BLEND_RANGE;
return 0.5f*normalized * normalized* normalized;  // }


R(uxx find_nearest_boundary_cell(const uint3 xyz) {
//const int dist_left = (int)xyz.x;
//const int dist_right = (int)def_Nx - 1 - (int)xyz.x; // bufferzone on y and z boundaies
const int dist_front = (int)xyz.y;
const int dist_back = (int)def_Ny - 1 - (int)xyz.y;
const int dist_bottom = (int)xyz.z;
const int dist_top = (int)def_Nz - 1 - (int)xyz.z;

int min_dist = dist_front;
int boundary_dir = 2;

//if(dist_right < min_dist) { min_dist = dist_right; boundary_dir = 1; }
//if(dist_front < min_dist) { min_dist = dist_front; boundary_dir = 2; }
if(dist_back < min_dist) { min_dist = dist_back; boundary_dir = 3; }
if(dist_bottom < min_dist) { min_dist = dist_bottom; boundary_dir = 4; }
if(dist_top < min_dist) { min_dist = dist_top; boundary_dir = 5; }

switch(boundary_dir) {
    //case 0: return index((uint3)(0u, xyz.y, xyz.z));
    //case 1: return index((uint3)(def_Nx-1u, xyz.y, xyz.z));
    case 2: return index((uint3)(xyz.x, 0u, xyz.z));
    case 3: return index((uint3)(xyz.x, def_Ny-1u, xyz.z));
    case 4: return index((uint3)(xyz.x, xyz.y, 0u));
    case 5: return index((uint3)(xyz.x, xyz.y, def_Nz-1u));
    default: return index((uint3)(0u, xyz.y, xyz.z));
}}
`

Change in void stream_collide:

`)+"#ifndef EQUILIBRIUM_BOUNDARIES"+R(
calculate_rho_u(fhn, &rhon, &uxn, &uyn, &uzn);
)+"#else"+R( // EQUILIBRIUM_BOUNDARIES
if(flagsn_bo==TYPE_E) {
    rhon = rho[               n];
    uxn  = u[                 n];
    uyn  = u[    def_N+(ulong)n];
    uzn  = u[2ul*def_N+(ulong)n];
} else {
    calculate_rho_u(fhn, &rhon, &uxn, &uyn, &uzn);
    
    const uint3 xyz = coordinates(n);
    // compute_type_e_blend_factor
    const float blend_factor = compute_type_e_blend_factor_simple(xyz);
    
    // find_nearest_boundary
    if(blend_factor < 0.9999f) {
        const uxx type_e_cell = find_nearest_boundary_cell(xyz);
        
        const float rho_type_e = rho[               type_e_cell];
        const float ux_type_e  = u[                 type_e_cell];
        const float uy_type_e  = u[    def_N+(ulong)type_e_cell];
        const float uz_type_e  = u[2ul*def_N+(ulong)type_e_cell];
        
        // apply bufferzone
        rhon = fma(rho_type_e, 1.0f - blend_factor, blend_factor * rhon);
        uxn  = fma(ux_type_e,  1.0f - blend_factor, blend_factor * uxn);
        uyn  = fma(uy_type_e,  1.0f - blend_factor, blend_factor * uyn);
        uzn  = fma(uz_type_e,  1.0f - blend_factor, blend_factor * uzn);
    }
    })+"#endif"+R( // EQUILIBRIUM_BOUNDARIES`

While the buffer zone can reduce reflections from the initial acoustic pressure, I have not yet established a benchmark case to perform parameter variation studies.

At now, I have no idea how to add a point source in the simulation and how to record the pressure on the observer point. Maybe I will update the benchmark cases in the few days.

Start with stream_collide and the proposed buffer-zone helpers in the issue text. Review the existing benchmark cases, then determine how a point source and observer pressure should be represented; done requires a reproducible acoustic benchmark and parameter comparison showing reduced TYPE_E reflection.