How to solve a system of parabolic partial differential equations in time and 1 D space

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Lucy 2017-11-22

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https://ww2.mathworks.cn/matlabcentral/answers/368494-how-to-solve-a-system-of-parabolic-partial-differential-equations-in-time-and-1-d-space

评论： Lucy 2017-11-22

采纳的回答： Torsten

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Hi,

I cannot seem to solve the PDF in the figures below. This is the code I have but it produces the wrong graphs:

function New
m=0;
x=0:0.5:15;
t=1:100:28800;
sol = pdepe(m,@pdefun,@icfun,@bcfun,x,t);
u1=sol(:,:,1);
u2=sol(:,:,2);
surf(x,t,u1)
title('u1(x,t)')
xlabel('Distance x')
ylabel('Time t')
figure
surf(x,t,u2)
title('u2(x,t)')
xlabel('Distance x')
ylabel('Time t')
function [c,f,s]=pdefun(x,t,u,DuDx)
P=1200;
R=0.208;
cv=0.313;
rho=7.5;
v=0.3;
A=70;
mdot=1.2;
k=0.016/1000;
alph=0.5;
rhoG=1600;
cG=0.7;
kG=0.7/1000;
c=[((P*cv/R)/u(1));(rhoG*cG)];
f=[((k*DuDx(1))-((P*cv/R)*(mdot*R/(P*A))));(kG*DuDx(2))];
s=[(u(2)-u(1));(u(1)-u(2))]*alph;
function u0=icfun(x)
u0=[300;300];
function[pl,ql,pr,qr]=bcfun(xl,ul,xr,ur,t)
pl = [ul(1)-773; 0]; 
ql = [0; 1]; 
pr = [0; 0]; 
qr = [1; 1];

I think my boundary conditions are incorrect but I don't know how to fit them.

I would appreciate any help with this problem, thank you in advance.

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采纳的回答

Torsten 2017-11-22

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/368494-how-to-solve-a-system-of-parabolic-partial-differential-equations-in-time-and-1-d-space#answer_292522

在 MATLAB Online 中打开

One mistake in your settings:

f = [k*DuDx(1) ; kG*DuDx(2)];
s = [(u(2)-u(1))*alph-cv*mdot/A*DuDx(1);(u(1)-u(2))*alph];

And maybe in your boundary condition for T_A at x=0, you will need a ramp that linearly increases the temperature from 300 K to 773 K in, say, one minute.

Best wishes

Torsten.