# 流体模拟“爆炸”

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``````#include <SDL2/SDL.h>
#include <stdio.h>
#include <iostream>
#include <algorithm>

#define IX(i,j) ((i)+(N+2)*(j))
using namespace std;

// Constants
const int SCREEN_WIDTH = 600;
const int SCREEN_HEIGHT = 600;  // Should match SCREEN_WIDTH
const int N = 20;               // Grid size
const int SIM_LEN = 1000;
const int DELAY_LENGTH = 40;    // ms

const float VISC = 0.01;
const float dt = 0.1;
const float DIFF = 0.01;

const bool DISPLAY_CONSOLE = false; // Console or graphics
const bool DRAW_GRID = false; // implement later

const int nsize = (N+2)*(N+2);
``````

``````void set_bnd(int N, int b, vector<float> &x)
{
// removed
}

inline void lin_solve(int N, int b, vector<float> &x, vector<float> &x0, float a, float c)
{
for (int k=0; k<20; k++)
{
for (int i=1; i<=N; i++)
{
for (int j=1; j<=N; j++)
{
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_bnd ( N, b, x );
}
}

void add_source(vector<float> &x, vector<float> &s, float dt)
{
for (int i=0; i<nsize; i++) x[i] += dt*s[i];
}

// Diffusion with Gauss-Seidel relaxation
void diffuse(int N, int b, vector<float> &x, vector<float> &x0, float diff, float dt)
{
float a = dt*diff*N*N;
lin_solve(N, b, x, x0, a, 1+4*a);

}

void advect(int N, int b, vector<float> &d, vector<float> &d0, vector<float> &u, vector<float> &v, float dt)
{
float dt0 = dt*N;
for (int i=1; i<=N; i++)
{
for (int j=1; j<=N; j++)
{
float x = i - dt0*u[IX(i,j)];
float y = j - dt0*v[IX(i,j)];
if (x<0.5) x=0.5; if (x>N+0.5) x=N+0.5;
int i0=(int)x; int i1=i0+1;
if (y<0.5) y=0.5; if (y>N+0.5) y=N+0.5;
int j0=(int)y; int j1=j0+1;

float s1 = x-i0; float s0 = 1-s1; float t1 = y-j0; float t0 = 1-t1;
d[IX(i,j)] = s0*(t0*d0[IX(i0,j0)] + t1*d0[IX(i0,j1)]) +
s1*(t0*d0[IX(i1,j0)] + t1*d0[IX(i1,j1)]);
}
}
set_bnd(N, b, d);
}
}

void project(int N, vector<float> &u, vector<float> &v, vector<float> &p, vector<float> &div)
{
float h = 1.0/N;
for (int i=1; i<=N; i++)
{
for (int j=1; j<=N; j++)
{
div[IX(i,j)] = -0.5*h*(u[IX(i+1,j)] - u[IX(i-1,j)] +
v[IX(i,j+1)] - v[IX(i,j-1)]);
p[IX(i,j)] = 0;
}
}
set_bnd(N, 0, div); set_bnd(N, 0, p);

lin_solve(N, 0, p, div, 1, 4);

for (int i=1; i<=N; i++)
{
for (int j=1; j<=N; j++)
{
u[IX(i,j)] -= 0.5*(p[IX(i+1,j)] - p[IX(i-1,j)])/h;
v[IX(i,j)] -= 0.5*(p[IX(i,j+1)] - p[IX(i,j-1)])/h;
}
}
set_bnd(N, 1, u); set_bnd(N, 2, v);
}
``````

``````// Density solver
void dens_step(int N, vector<float> &x, vector<float> &x0, vector<float> &u, vector<float> &v, float diff, float dt)
{
swap(x0, x); diffuse(N, 0, x, x0, diff, dt);
swap(x0, x); advect(N, 0, x, x0, u, v, dt);
}

void vel_step(int N, vector<float> &u, vector<float> &v, vector<float> &u0, vector<float> &v0, float visc, float dt)
{
swap(u0, u); diffuse(N, 1, u, u0, visc, dt);
swap(v0, v); diffuse(N, 2, v, v0, visc, dt);
project(N, u, v, u0, v0);
swap(u0, u); swap(v0, v);
advect(N, 1, u, u0, u0, v0, dt); advect(N, 2, v, v0, u0, v0, dt);
project(N, u, v, u0, v0);
}
``````

Iwillnotexist Idonotexist

``````x[i] = (x[i]+dt*s[i])/(1.0f+dt);
``````

，或计算as`c`参数要么将迫使质量下降。`lin_solve()``1+4*a+dt`

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