Question

我正在尝试制作一个模拟Processing中流体物理的程序。在IDE中有一个包含的示例：

    /**
     * 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);
      }

}

它没有真正评论过，我对编程有点新意，所以我不知道从哪里开始理解它。关于流体物理学是否有任何好的阅读？我对视觉效果比模拟的准确性更有趣。

Answer 1

一个好的起点可能是论文Stable Fluids，它将向您展示流体模拟背后的数学，在第三章中它描述了流体求解器的实现。 sourceforge中还有一个open source implementation（您需要使用cvs检查源代码）。

谁能帮我理解如何模拟液体？

1 个答案: