//Fluid vs Structure 2d

//v velocity, sx and sy stresses

//dv/dt = dsx/dx+dsy/dy (Newton 2nd law)

//dsx/dt=dv/dx, dsy/dt=dv/dy elastic stress rate vs strain rate: Wave equation

//sx=dv/dx, sy=dv/dy viscous stress vs strain rate: Viscous flow equation 

let sx= [];

let sy= [];

let v= [];

let u = [];

let M = 100;

let h=1/M;

let dt=0.2*h;

let S=1;

let colorgradient = ['#ff5500','#ff4f0e','#ff4817','#ff411f','#fe3a25','#fe332a','#fd2a30','#fc2135','#fa1539','#f9023e','#f70042','#f50046','#f3004a','#f0004e','#ed0052','#ea0056','#e7005a','#e4005e','#e00062','#dc0065','#d80069','#d4006c','#d00070','#cb0073','#c60076','#c10079','#bc007c','#b6007f','#b00082','#aa0084','#a40087','#9e0089','#97008b','#91008d','#8a008f','#820090','#7b0892','#730f93','#6b1594','#621995'];

let gradstep ;

let gradnuances = [];

​

function setup() {

  createCanvas(450,450);

  gradstep = 100/colorgradient.length;

  // gradnuances = [];

  for (var i=0 ; i<colorgradient.length; i++){

    gradnuances.push(i*gradstep);

  }

  for (var i=0;i<M;i++){

    sx[i]=[];

    sy[i]=[];

    v[i]=[];

    u[i]=[];

}

​

for (var i=0;i<M;i++){

for (var j=0;j<M;j++){

sx[i][j]=0;

sy[i][j]=0;

v[i][j]=0;

u[i][j]=0;

}

}

//initial data

//for (m=45;m<55;m++){

//for (n=0;n<M;n++){

//v[m][n]=1;

for (m=0;m<10;m++){

for (n=0;n<10;n++){

v[46+m][46+n]=1;

}

}

}

​

​

function draw(){

//background('#621995');

​

for (var i=1;i<M-1;i++){

for (var j=1;j<M-1;j++){

//structure

if (S==1){

sx[i][j]=sx[i][j]+dt*(v[i][j]-v[i-1][j])/h;

sy[i][j]=sy[i][j]+dt*(v[i][j]-v[i][j-1])/h;

}

//fluid

if (S==0){

sx[i][j]=h*(v[i][j]-v[i-1][j])/h;

sy[i][j]=h*(v[i][j]-v[i][j-1])/h;

}

v[i][j] = v[i][j] + dt*(sx[i+1][j]-sx[i][j]+sy[i][j+1]-sy[i][j])/h+0.1*dt*(v[i+1][j]+v[i-1][j]+v[i][j+1]+v[i][j-1]-4*v[i][j])/h;

u[i][j]=u[i][j]+dt*v[i][j];

}

}

​

noStroke();

for (var i=0;i<M;i++){

for (var j=0;j<M;j++){

  for(var k = 0 ; k<colorgradient.length ; k++){

    if(2*255*abs(v[i][j]) >= gradnuances[k]){

      c = color(colorgradient[k]);

      c.setAlpha(2*255*abs(v[i][j]));

      fill(c);

    }

  }

// fill(255,0,0,2*255*abs(v[i][j]));

rect(4*i,4*j,4,4);

//}

}

}

​

// for (var i=1;i<M-1;i++){

// fill(0);

// ellipse(4*i,200+800*v[i][50],3);

// fill(0,0,255,255);

// ellipse(4*i,200+800*u[i][50],3);

// ellipse(4*i,200,2);

// }

// fill(0);

// text("Fluid-Structure 2d: v velocity, sx and sy stresses",100,10);

// text("S=1: Elastic Structure: Wave equation: dv/dt = dsx/dx + dsy/dy (Newton 2nd law)",20,40)

// text("dsx/dt = dv/dx, dsy/dt=dv/dy (stress rate vs strain rate)",20,60);

// text("S=0: Viscous Fluid: dv/dt = dsx/dx + dsy/dy (Newton's 2nd Law)",20,90);

// text("sx = dv/dx, sy=dv/dy (stress vs strain rate)",20,110);

// text("(u displacement small for structure, du/dt=v)",20,260);

// text("Structure: Elastic membrane.",20,350);

// text("Play with other initial data.",20,150);

// text("velocity v: black, displacement u: blue (crosscut)",20,300);

}