數學建模美賽集訓的時候要用到一個海面模擬，分享一下海面模擬的MATLAB代碼

先貼一下結果圖：

下面是源代碼~~~

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');

PhoenixFD插件流體模擬——UI布局【Dynamics】詳解

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