海面波浪模拟 MATLAB

数学建模美赛集训的时候要用到一个海面模拟，分享一下海面模拟的MATLAB代码

先贴一下结果图：

下面是源代码~~~

 function waterwave

 n = 64;                  % grid size
 g = 9.8;                 % gravitational constant
 dt = 0.01;               % hardwired timestep
 dx = 1.0;
 dy = 1.0;
 nplotstep = 8;           % plot interval
 ndrops = 5;              % maximum number of drops
 dropstep = 500;          % drop interval
 D = droplet(1.5,21);     % simulate a water drop

 % Initialize graphics

 [surfplot,top,start,stop] = initgraphics(n);

 % Outer loop, restarts.

 while get(stop,'value') == 0
    set(start,'value',0)

    H = ones(n+2,n+2);   U = zeros(n+2,n+2);  V = zeros(n+2,n+2);
    Hx = zeros(n+1,n+1); Ux = zeros(n+1,n+1); Vx = zeros(n+1,n+1);
    Hy = zeros(n+1,n+1); Uy = zeros(n+1,n+1); Vy = zeros(n+1,n+1);
    ndrop = ceil(rand*ndrops);
    nstep = 0;

    % Inner loop, time steps.

    while get(start,'value')==0 && get(stop,'value')==0
        nstep = nstep + 1;

        % Random water drops
        if mod(nstep,dropstep) == 0 && nstep <= ndrop*dropstep
            w = size(D,1);
            i = ceil(rand*(n-w))+(1:w);
            j = ceil(rand*(n-w))+(1:w);
            H(i,j) = H(i,j) + rand*D;
        end

        % Reflective boundary conditions
        H(:,1) = H(:,2);      U(:,1) = U(:,2);       V(:,1) = -V(:,2);
        H(:,n+2) = H(:,n+1);  U(:,n+2) = U(:,n+1);   V(:,n+2) = -V(:,n+1);
        H(1,:) = H(2,:);      U(1,:) = -U(2,:);      V(1,:) = V(2,:);
        H(n+2,:) = H(n+1,:);  U(n+2,:) = -U(n+1,:);  V(n+2,:) = V(n+1,:);

        % First half step

        % x direction
        i = 1:n+1;
        j = 1:n;

        % height
        Hx(i,j) = (H(i+1,j+1)+H(i,j+1))/2 - dt/(2*dx)*(U(i+1,j+1)-U(i,j+1));

        % x momentum
        Ux(i,j) = (U(i+1,j+1)+U(i,j+1))/2 -  ...
                  dt/(2*dx)*((U(i+1,j+1).^2./H(i+1,j+1) + g/2*H(i+1,j+1).^2) - ...
                             (U(i,j+1).^2./H(i,j+1) + g/2*H(i,j+1).^2));

        % y momentum
        Vx(i,j) = (V(i+1,j+1)+V(i,j+1))/2 - ...
                  dt/(2*dx)*((U(i+1,j+1).*V(i+1,j+1)./H(i+1,j+1)) - ...
                             (U(i,j+1).*V(i,j+1)./H(i,j+1)));

        % y direction
        i = 1:n;
        j = 1:n+1;

        % height
        Hy(i,j) = (H(i+1,j+1)+H(i+1,j))/2 - dt/(2*dy)*(V(i+1,j+1)-V(i+1,j));

        % x momentum
        Uy(i,j) = (U(i+1,j+1)+U(i+1,j))/2 - ...
                  dt/(2*dy)*((V(i+1,j+1).*U(i+1,j+1)./H(i+1,j+1)) - ...
                             (V(i+1,j).*U(i+1,j)./H(i+1,j)));
        % y momentum
        Vy(i,j) = (V(i+1,j+1)+V(i+1,j))/2 - ...
                  dt/(2*dy)*((V(i+1,j+1).^2./H(i+1,j+1) + g/2*H(i+1,j+1).^2) - ...
                             (V(i+1,j).^2./H(i+1,j) + g/2*H(i+1,j).^2));

        % Second half step
        i = 2:n+1;
        j = 2:n+1;

        % height
        H(i,j) = H(i,j) - (dt/dx)*(Ux(i,j-1)-Ux(i-1,j-1)) - ...
                          (dt/dy)*(Vy(i-1,j)-Vy(i-1,j-1));
        % x momentum
        U(i,j) = U(i,j) - (dt/dx)*((Ux(i,j-1).^2./Hx(i,j-1) + g/2*Hx(i,j-1).^2) - ...
                          (Ux(i-1,j-1).^2./Hx(i-1,j-1) + g/2*Hx(i-1,j-1).^2)) ...
                        - (dt/dy)*((Vy(i-1,j).*Uy(i-1,j)./Hy(i-1,j)) - ...
                          (Vy(i-1,j-1).*Uy(i-1,j-1)./Hy(i-1,j-1)));
        % y momentum
        V(i,j) = V(i,j) - (dt/dx)*((Ux(i,j-1).*Vx(i,j-1)./Hx(i,j-1)) - ...
                          (Ux(i-1,j-1).*Vx(i-1,j-1)./Hx(i-1,j-1))) ...
                        - (dt/dy)*((Vy(i-1,j).^2./Hy(i-1,j) + g/2*Hy(i-1,j).^2) - ...
                          (Vy(i-1,j-1).^2./Hy(i-1,j-1) + g/2*Hy(i-1,j-1).^2));

        % Update plot
        if mod(nstep,nplotstep) == 0
           C = abs(U(i,j)) + abs(V(i,j));  % Color shows momemtum
           t = nstep*dt;
           tv = norm(C,'fro');
           set(surfplot,'zdata',H(i,j),'cdata',C);
           set(top,'string',sprintf('t = %6.2f,  tv = %6.2f',t,tv))
           drawnow
        end

        if all(all(isnan(H))), break, end  % Unstable, restart
    end
 end
 close(gcf)

 % ------------------------------------

 function D = droplet(height,width)
 % DROPLET  2D Gaussian
 % D = droplet(height,width)
    [x,y] = ndgrid(-1:(2/(width-1)):1);
    D = height*exp(-5*(x.^2+y.^2));

 % ------------------------------------

 function [surfplot,top,start,stop] = initgraphics(n);
 % INITGRAPHICS  Initialize graphics for waterwave.
 % [surfplot,top,start,stop] = initgraphics(n)
 % returns handles to a surface plot, its title, and two uicontrol toggles.

    clf
    shg
    set(gcf,'numbertitle','off','name','Shallow_water')
    x = (0:n-1)/(n-1);
    surfplot = surf(x,x,ones(n,n),zeros(n,n));
    grid off
    axis([0 1 0 1 -1 3])
    caxis([-1 1])
    shading faceted
    c = (1:64)'/64;
    cyan = [0*c c c];
    colormap(cyan)
    top = title('Click start');
    start = uicontrol('position',[20 20 80 20],'style','toggle','string','start');
    stop = uicontrol('position',[120 20 80 20],'style','toggle','string','stop');