Solving multiple PDE with using PDEPE
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Hi guys,
I have a trouble to use pdepe. I want to solve 4 different partial differential equation and here is the my boundary conditions. Here is the my problem's physical setup.
Acoording to this physical setup here is the my boundary conditions.
Here is the my initial condition.
And my pdes are:
L = 1500; %lenght
x = linspace(0,L,1501); %x values from 0 to 1000 and dx=1 meter
t = linspace(0,10,11); %t values from 0 to 10 and dt=1 day
m = 0;
%coordinate and it is also explained in the form of pdepe
sol = pdepe(m,@headpde,@headic,@headbc,x,t);%solution of head partial dif. equ. with
colormap hot %
imagesc(x,t,sol) %
colorbar % Graph of the t<=0 to t<=20
hold on %
xlabel('Distance x','interpreter','latex') %
ylabel('Time t','interpreter','latex') %
title('Head Distribution for $0 \le x \le 1500$ and $0 \le t \le 10$','interpreter','latex')
function [c,f,s] = headpde(x,t,u,dudx)
c = [6.67*10^-4;5*10^-4;4*10^-4;3.33*10^-4];
f = [1;1;1;1].*dudx;
s = [0;2*10^-6;4*10^-6;0];
end
function u0 = headic(x) %initial condition of pde
u0 = (-2/150*x)+60; % equation of initial condition
end
function [pl,ql,pr,qr] = headbc(xl,ul,xr,ur,t) %Boundary condition of pde
pl = ul-60; %Left side boundary condition is fixed and %it is equal to 60 this line represents that
ql = 0;
pr = ur-40; %Right side boundary condition is fixed and %it is equal to 40
qr = 0; %qr shows that again in the right side of %the boundary condition
end
I wrote this code for only t is between 0 to 10 days. But it gives errors. For this reason I will be grateful if you could help me!
P.S. I'm a new learner that's why if you be kind to me I would be appreciate :)
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Accepted Answer
Torsten
on 2 Jun 2022
Edited: Torsten
on 4 Jun 2022
L = 1500; %lenght
x = linspace(0,L,1501); %x values from 0 to 1000 and dx=1 meter
t = linspace(0,20,21); %t values from 0 to 10 and dt=1 day
m = 0; %coordinate and it is also explained in the form of pdepe
sol = pdepe(m,@headpde,@headic,@headbc,x,t);%solution of head partial dif. equ. with
colormap hot %
imagesc(x,t,sol) %
colorbar % Graph of the t<=0 to t<=20
hold on %
xlabel('Distance x','interpreter','latex') %
ylabel('Time t','interpreter','latex') %
title('Head Distribution for $0 \le x \le 1500$ and $0 \le t \le 10$','interpreter','latex')
function [pl,ql,pr,qr] = headbc(xl,ul,xr,ur,t) %Boundary condition of pde
if t <= 10
pl = ul - 60;
ql = 0.0;
else
pl = ul - (60-(t-10));
ql = 0.0;
end
pr = ur - 40;
qr = 0;
end
function [c,f,s] = headpde(x,t,u,dudx)
if x <= 500
c = 6.67e-4;
f = dudx;
s = 0;
elseif x > 500 && x <=800
c = 5e-4;
f = dudx;
s = 2e-6;
elseif x > 800 && x <= 1100
c = 4e-4;
f = dudx;
s = 4e-6;
else
c = 3.33e-4;
f = dudx;
s = 0.0;
end
end
function ic = headic(x)
ic = -2/150*x + 60;
end
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