I'm trying to create my own CFD in C++. I have watched some videos on youtube about the Lattice Boltzmann method, but I cant get my simulations to look like the simulations performed in the videos with lattice Boltzmann implemented in Python.
I use SDL2 to create an image on my screen. I am not trying to create anything fast. Just something that will make pretty simulations on the CPU.
Here is my class for each cell:
//cell class
class cell {
public:
double Fi[nL] = {0,0,0,0,0,0,0,0,0};
double density = 0;
double momentumX = 0;
double momentumY = 0;
double velocityX = 0;
double velocityY = 0;
double Fieq[nL] = {0,0,0,0,0,0,0,0,0};
//obstacle
bool obstacle = false;
void densityOperator() {
for (int i = 0; i < nL; i++) {
density += Fi[i];
}
}
void momentumOperator() {
for (int i = 0; i < nL; i++) {
momentumX += Fi[i] * cX[i];
momentumY += Fi[i] * cY[i];
}
}
void velocityOperator() {
for (int i = 0; i < nL; i++) {
if (density == 0) {
density += 0.001;
}
velocityX += momentumX / density; // prolly very slow
velocityY += momentumY / density;
//velocityX += cX[i];
//velocityY += cY[i];
}
}
void FieqOperator() {
for (int i = 0; i < nL; i++) {
Fieq[i] = weights[i] * density *
(
1 +
(cX[i] * velocityX + cY[i] * velocityY) / Cs +
pow((cX[i] * velocityX + cY[i] * velocityY), 2) / (2 * pow(Cs, 4)) -
(velocityX * velocityX + velocityY * velocityY) / (2 * pow(Cs, 2))
);
}
}
void FiOperator() {
for (int i = 0; i < nL; i++) {
Fi[i] = Fi[i] - (timestep / tau) * (Fi[i] - Fieq[i]);
}
}
void addRightVelocity() {
Fi[0] = 1.f;
Fi[1] = 1.f;
Fi[2] = 1.f;
Fi[3] = 6.f;
Fi[4] = 1.f;
Fi[5] = 1.f;
Fi[6] = 1.f;
Fi[7] = 1.f;
Fi[8] = 1.f;
}
};
Please note that im am using a vector for my cells instead of a 2d array. I am using a index function to go from x,y to 1d cordinate.
int index(int x, int y) {
return x * nY + y;
}
Variables:
//box
const int nX = 400;
const int nY = 100;
//viscosity
float tau = 0.5; // 0.53
//time delta time per iteration
float timestep = 1;
//distance between cells
float dist = 1000;
//Speed of sound
float Cs = 1 / sqrt(3) * (dist / timestep);
//viscociti
float v = pow(Cs, 2) * (tau - timestep / 2); // tau will need to be much smaller
//time steps
int nT = 3000;
//lattice speeds and weights
const int nL = 9;
//Ci vector direction, discrete velocity
int cX[9] = { 0, 0, 1, 1, 1, 0, -1, -1, -1 };
int cY[9] = { 0, 1, 1, 0, -1, -1, -1, 0 , 1 };
//weights, based on navier stokes
float weights[9] = { 4 / 9, 1 / 9, 1 / 36, 1 / 9, 1 / 36, 1 / 9, 1 / 36, 1 / 4, 1 / 36 };
//opposite populations
int cO[9] = { 0, 5, 6, 7, 8, 1, 2, 3, 4 };
My main function:
int main() {
//init vector cells
for (int x = 0; x < nX; x++) {
for (int y = 0; y < nY; y++) {
cell cellUnit;
cells.push_back(cellUnit);
TempCells.push_back(cellUnit);
}
}
//SDL
//SDL
//-------------------------------------------------------------
SDL_Window* window = nullptr;
SDL_Renderer* renderer = nullptr;
SDL_Init(SDL_INIT_VIDEO);
SDL_CreateWindowAndRenderer(nX* 3, nY * 3, 0, &window, &renderer);
SDL_RenderSetScale(renderer, 3, 3);
SDL_SetRenderDrawColor(renderer, 0, 0, 0, 255);
SDL_RenderClear(renderer);
//-------------------------------------------------------------//
//Circle Object Gen
for (int x = 0; x < nX; x++) {
for (int y = 0; y < nY; y++) {
//cicle position
int circleX = 5;
int circleY = 50;
//circle radius
float radius = 10;
//distance bewtween cell and circle pos
float distance = sqrt(pow(circleX - x, 2) + pow(circleY - y, 2));
if (distance < radius) {
cells[index(x,y)].obstacle = true;
}
else {
cells[index(x, y)].obstacle = false;
}
}
}
//add velocity
for (int x = 0; x < nX; x++) {
for (int y = 0; y < nY; y++) {
cells[index(x, y)].addRightVelocity();
//random velocity
for (int i = 0; i < nL; i++) {
cells[index(x,y)].Fi[i] += (rand() % 200) / 100;
}
}
}
for (int t = 0; t < nT; t++) {
//SDL
//--------------------------------------------------------------
//clear renderer
if (t % 20 == 0) {
SDL_SetRenderDrawColor(renderer, 255, 255, 255, 255);
SDL_RenderClear(renderer);
}
//--------------------------------------------------------------
//streaming:
//because we will loop over the same populations we do not want to switch the same population twice
for (int x = 0; x < nX; x++) {
for (int y = 0; y < nY; y++) {
if (x == 0) {
cells[index(x, y)].Fi[3] += 0.4;
}
//for populations
for (int i = 0; i < nL; i++) {
//boundary
//checs if cell is object or air
if (cells[index(x, y)].obstacle == false) {
//air
//targetet cell
int cellX = x + cX[i];
int cellY = y + cY[i];
//out of bounds check + rearange to other side
if (cellX < 0) {
//left to right
cellX = nX;
}
if (cellX >= nX) {
//right to left
cellX = 0;
continue;
}
if (cellY < 0) {
//top to buttom
cellY = nY;
}
if (cellY >= nY) {
//bottom to top
cellY = 0;
}
//if neighborinig cell is object --> collision with object
if (cells[index(cellX, cellY)].obstacle == true) {
//Boundary handling https://youtu.be/jfk4feD7rFQ?t=2821
TempCells[index(x,y)].Fi[cO[i]] = cells[index(x, y)].Fi[i];
}
//if not then stream to neighbor air cell with oposite population
TempCells[index(cellX, cellY)].Fi[cO[i]] = cells[index(x, y)].Fi[i];
}
else {
//wall
//SDL GRAPICHS
if (t % 20 == 0) {
SDL_SetRenderDrawColor(renderer, 0, 0, 0, 255);
SDL_RenderDrawPoint(renderer, x, y);
}
}
}
}
}
for (int x = 0; x < nX; x++) {
for (int y = 0; y < nY; y++) {
for (int i = 0; i < nL; i++) {
cells[index(x, y)].Fi[i] = TempCells[index(x, y)].Fi[cO[i]];
}
}
}
//collision:
for (int x = 0; x < nX; x++) {
for (int y = 0; y < nY; y++) {
//density:
cells[index(x, y)].densityOperator();
//momentum:
cells[index(x, y)].momentumOperator();
//velocity:
cells[index(x, y)].velocityOperator();
//Fieq + new new Fi:
for (int i = 0; i < nL; i++) {
cells[index(x, y)].FieqOperator();
}
//SDL Graphics
if (t % 20 == 0) {
if (cells[index(x, y)].obstacle == false) {
SDL_SetRenderDrawColor(renderer, cells[index(x, y)].density, cells[index(x, y)].density , 255 , 255);
SDL_RenderDrawPoint(renderer, x, y);
}
}
}
}
for (int x = 0; x < nX; x++) {
for (int y = 0; y < nY; y++) {
cells[index(x, y)].FiOperator();
}
}
//SDL Graphics
if (t % 20 == 0 ) {
SDL_RenderPresent(renderer);
}
}
return 0;
}
I do realize my code might be a bit messy and not easy to understand at first. And it is definitely not optimal.
If anyone has any experience in programming their own LBM in c++ i would like to hear your input.
It seams like my simulations is working but i do not get those bueatiful animations like in, https://youtu.be/ZUXmO4hu-20?t=3394
Thanks for any help.
Edit:
I have edited my script to reset, density, velocity X Y and Momentum X Y
Simulation visualised by density, pink is higher, loops if density exceeds color range of 255
