Solving multiple PDE with using PDEPE

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 :)

Answer 1

[Torsten]

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

[Sait Mutlu Karahan]

Hi Torsten! You are truly a life saver! Thanks for replying my two problems and thanks for your time! You really help me a lot! Thanks many times :)