任何人都可以幫助我理解如何模擬液體？

Question

我正在試着製作一個程序來模擬加工過程中的流體物理過程。在IDE中有一個附帶的例子：

/** 
    * Fluid 
    * by Glen Murphy. 
    * 
    * Click and drag the mouse to move the simulated fluid. 
    * Adjust the "res" variable below to change resolution. 
    * Code has not been optimised, and will run fairly slowly. 
    */ 

    int res = 2; 
    int penSize = 30; 
    int lwidth; 
    int lheight; 
    int pnum = 30000; 
    vsquare[][] v; 
    vbuffer[][] vbuf; 
    particle[] p = new particle[pnum]; 
    int pcount = 0; 
    int mouseXvel = 0; 
    int mouseYvel = 0; 

    void setup() 
    { 
     size(200, 200); 
     noStroke(); 
     frameRate(30); 
     lwidth = width/res; 
     lheight = height/res; 
     v = new vsquare[lwidth+1][lheight+1]; 
     vbuf = new vbuffer[lwidth+1][lheight+1]; 
     for (int i = 0; i < pnum; i++) { 
     p[i] = new particle(random(res,width-res),random(res,height-res)); 
     } 
     for (int i = 0; i <= lwidth; i++) { 
     for (int u = 0; u <= lheight; u++) { 
      v[i][u] = new vsquare(i*res,u*res); 
      vbuf[i][u] = new vbuffer(i*res,u*res); 
     } 
     } 
    } 

    void draw() 
    { 
     background(#666666); 

     int axvel = mouseX-pmouseX; 
     int ayvel = mouseY-pmouseY; 

     mouseXvel = (axvel != mouseXvel) ? axvel : 0; 
     mouseYvel = (ayvel != mouseYvel) ? ayvel : 0; 

     for (int i = 0; i < lwidth; i++) { 
     for (int u = 0; u < lheight; u++) { 
      vbuf[i][u].updatebuf(i,u); 
      v[i][u].col = 32; 
     } 
     } 
     for (int i = 0; i < pnum-1; i++) { 
     p[i].updatepos(); 
     } 
     for (int i = 0; i < lwidth; i++) { 
     for (int u = 0; u < lheight; u++) { 
      v[i][u].addbuffer(i, u); 
      v[i][u].updatevels(mouseXvel, mouseYvel); 
      v[i][u].display(i, u); 
     } 
     } 
    } 

    class particle { 
     float x; 
     float y; 
     float xvel; 
     float yvel; 
     int pos; 
     particle(float xIn, float yIn) { 
     x = xIn; 
     y = yIn; 
     } 

     void updatepos() { 
     float col1; 
     if (x > 0 && x < width && y > 0 && y < height) { 
      int vi = (int)(x/res); 
      int vu = (int)(y/res); 
      vsquare o = v[vi][vu];  

      float ax = (x%res)/res; 
      float ay = (y%res)/res; 

      xvel += (1-ax)*v[vi][vu].xvel*0.05; 
      yvel += (1-ay)*v[vi][vu].yvel*0.05; 

      xvel += ax*v[vi+1][vu].xvel*0.05; 
      yvel += ax*v[vi+1][vu].yvel*0.05; 

      xvel += ay*v[vi][vu+1].xvel*0.05; 
      yvel += ay*v[vi][vu+1].yvel*0.05; 

      o.col += 4; 

      x += xvel; 
      y += yvel; 
     } 
     else { 
      x = random(0,width); 
      y = random(0,height); 
      xvel = 0; 
      yvel = 0; 
     } 

     xvel *= 0.5; 
     yvel *= 0.5; 
     } 
    } 

    class vbuffer { 
     int x; 
     int y; 
     float xvel; 
     float yvel; 
     float pressurex = 0; 
     float pressurey = 0; 
     float pressure = 0; 

     vbuffer(int xIn,int yIn) { 
     x = xIn; 
     y = yIn; 
     pressurex = 0; 
     pressurey = 0; 
     } 

     void updatebuf(int i, int u) { 
     if (i>0 && i<lwidth && u>0 && u<lheight) { 
      pressurex = (v[i-1][u-1].xvel*0.5 + v[i-1][u].xvel + v[i-1][u+1].xvel*0.5 - v[i+1][u-1].xvel*0.5 - v[i+1][u].xvel - v[i+1][u+1].xvel*0.5); 
      pressurey = (v[i-1][u-1].yvel*0.5 + v[i][u-1].yvel + v[i+1][u-1].yvel*0.5 - v[i-1][u+1].yvel*0.5 - v[i][u+1].yvel - v[i+1][u+1].yvel*0.5); 
      pressure = (pressurex + pressurey)*0.25; 
      } 
     } 
     } 

    class vsquare { 
     int x; 
     int y; 
     float xvel; 
     float yvel; 
     float col; 

     vsquare(int xIn,int yIn) { 
     x = xIn; 
     y = yIn; 
     } 

     void addbuffer(int i, int u) { 
     if (i>0 && i<lwidth && u>0 && u<lheight) { 
      xvel += (vbuf[i-1][u-1].pressure*0.5 
        +vbuf[i-1][u].pressure 
        +vbuf[i-1][u+1].pressure*0.5 
        -vbuf[i+1][u-1].pressure*0.5 
        -vbuf[i+1][u].pressure 
        -vbuf[i+1][u+1].pressure*0.5 
       )*0.25; 
      yvel += (vbuf[i-1][u-1].pressure*0.5 
        +vbuf[i][u-1].pressure 
        +vbuf[i+1][u-1].pressure*0.5 
        -vbuf[i-1][u+1].pressure*0.5 
        -vbuf[i][u+1].pressure 
        -vbuf[i+1][u+1].pressure*0.5 
       )*0.25; 
      } 
     } 

     void updatevels(int mvelX, int mvelY) { 
     if (mousePressed) { 
      float adj = x - mouseX; 
      float opp = y - mouseY; 
      float dist = sqrt(opp*opp + adj*adj); 
      if (dist < penSize) { 
      if (dist < 4) dist = penSize; 
      float mod = penSize/dist; 
      xvel += mvelX*mod; 
      yvel += mvelY*mod; 
      } 
      } 

     xvel *= 0.99; 
     yvel *= 0.99; 
     } 

     void display(int i, int u) { 
     float tcol = 0; 
     if (col > 255) col = 255; 
     if (i>0 && i<lwidth-1 && u>0 && u<lheight-1) { 
      tcol = (+ v[i][u+1].col 
        + v[i+1][u].col 
        + v[i+1][u+1].col*0.5 
       )*0.4; 
      tcol = (int)(tcol+col*0.5); 
      } 
     else { 
      tcol = (int)col; 
      } 
     fill(tcol, tcol, tcol); 
     rect(x,y,res,res); 
     } 

} 

這不是真正的評論，我有點新的節目，所以我不知道從哪裏就開始爲理解它。流體物理學有什麼好的讀物嗎？在視覺效果方面，我比模擬的精確度更有趣。

Answer 1

一個好的起點可以是論文Stable Fluids，它會告訴你流體模擬背後的數學，並在第三章中描述流體求解器的實現。在sourceforge中還有一個open source implementation可用（你需要用CVS檢查源代碼）。