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clear all; close all; l=45; alpha1=-0.25; lambda1=0.25; n=128; x=l/n*[-n/2:n/2-1]; y=x; kx=(2*pi/l)*[0:n/2-1 -n/2:-1]; kx(1)=1e-6; ky=kx; [x,y]=meshgrid(x,y); [kx,ky]=meshgrid(kx,ky); h=2*pi/n; column=[00.5*(-1).^(1:n-1).*cot((1:n-1)*h/2)]'; d=(2*pi/l)*toeplitz(column,column([1n:-1:2])); column=[-pi^2/(3*h^2)-1/6-0.5*(-1).^(1:n-1)./sin(h*(1:n-1)/2).^2]; d2=(2*pi/l)^2*toeplitz(column); column=[0 (-1).^(1:n-1).*cot((1:n-1)*h/2).*(-pi^2/(2*h^2)+3/4*csc((1:n-1)*h/2).^2)]'; w=1+0.1*cos(0.31*x)+0.1*cos(0.31*y);%³õʼÌõ¼þ t=[0 17 17.5 18 19 20 21 22 23 25 30 40] [t,wsol]=ode45('advection_diffusion', t, w( : ),[],n,d,d2,alpha1,lambda1,x); advection_diffusion.m function dw=advection_diffusion(t,w,dummy,n,d,d2,alpha1,lambda1, x); w=reshape(w,n,n); wt=fft2(w); if (t<=20) dw=reshape(i*(alpha1*d2*w+lambda1*w*d2')+t,n^2,1); else dw=reshape(i*(alpha1*d2*w+lambda1*w*d2')-t,n^2,1); end ÎÒÏëÇó½âÒ»¸öƫ΢·Ö·½³Ì£¬±äÁ¿t È¡ÁË12¸öÖµ£¬ÔÚ±»µ÷Óõĺ¯Êý advection_diffusion ÖÐÐèÒªÓõ½Ò»¸ö if Óï¾ä£¬¶Ô t½øÐзÖÀ࣬³ÌÐòÒ»Ö±ÔËÐв»³öÀ´¡£Ï£ÍûµÃµ½´ó¼ÒµÄÖ¸µã£¬²»Ê¤¸Ð¼¤¡£ |
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