onde.edp

FreeFem++可以生成高质量的有限元网格。可以用于流体力学

int i, N=20;
mesh Th=square(N,N);
fespace RTh(Th,RT0);
fespace P0h(Th,P0);
fespace P1h(Th,P1);

RTh [Vx,Vy],[vx,vy];
P0h up,u,um;

real dt=0.125/N, pi=4*atan(1.0);
[Vx,Vy]=[0,0];
um= sin(pi*x)*sin(pi*y);
u=um;

problem prob(Vx,Vy,vx,vy,solver=Cholesky,init=i)
    = int2d(Th) (Vx*vx+Vy*vy) + int2d(Th)(up*(dx(vx)+dy(vy)))
//     + on(1,2,3,4,Vx=pi*cos(pi*x)*sin(pi*y)*cos(i*dt*pi*sqrt(2.))
//                 ,Vy=pi*sin(pi*x)*cos(pi*y)*cos(i*dt*pi*sqrt(2.)) )
;
for (i=0;i<20;i++)
 {
     up = 2*u-um+dt*dt*(dx(Vx)+dy(Vy));
     prob;
     um=u;
     u=up;
     cout<< int2d(Th)((u-sin(pi*x)*sin(pi*y)*cos(i*dt*pi*sqrt(2.)))^2)
     /int2d(Th)((sin(pi*x)*sin(pi*y)*cos(i*dt*pi*sqrt(2.)))^2)<< endl;
//     plot([Vx,Vy],wait=0, value=1);
 }
P1h w,W = 0;
problem prob1(W,w,solver=Cholesky,init=0)
    = int2d(Th) (W*w) + int2d(Th)(up*w);
    prob1;
    plot(W,wait=1,value=1);