Solving advection diffusion pde

I want to solve the above pde with the given boundary and initial conditions. I came across the pdepe function in MATLAB.

I had a chance to look at the example given here . I couldn't understand how pdex1pde function has to be defined for my case.

Could someone help?

[Deepa Maheshvare]

Hi All,

Is the following implementation correct?

function DiffusionConvection
m = 0;
x = linspace(0,62,10);
t = linspace(0,10,100);

sol = pdepe(m,@pdefun,@icfun,@bcfun,x,t)

function [g,f,s] = pdefun(x,t,c,DcDx)
D = 900;
v = 10;
g = 1;
f = D*DcDx;
s = -v*DcDx;
end

function c0 = icfun(x)
c0 = 80;
end

function [pl,ql,pr,qr] = bcfun(xl,cl,xr,cr,t)
pl = cl -10;
ql = 1;
pr = cr;
qr = 1;
end
end

Answer 1

[Bill Greene]

The only problem I see with your code is in the boundary conditions. I corrected your bcfun function and have attached my version of your code below.

function DiffusionConvection
m = 0;
x = linspace(0,62,10);
t = linspace(0,10,100);
D = 900;
sol = pdepe(m,@pdefun,@icfun,@bcfun,x,t);

    function [g,f,s] = pdefun(x,t,c,DcDx)
    v = 10;
    g = 1;
    f = D*DcDx;
    s = -v*DcDx;
    end
    
    function c0 = icfun(x)
    c0 = 80;
    end
    
    function [pl,ql,pr,qr] = bcfun(xl,cl,xr,cr,t)
    pl = -10*D;
    ql = 1;
    pr = 0;
    qr = 1;
    end

end

[Deepa Maheshvare]

Should it be

    pl = cl - 10*D
    
%     Could you please explain?

[Bill Greene]

Equation 3 on this page, pdepe, shows the boundary condition form required. I simply matched terms from the BCs you defined above.

[Deepa Maheshvare]

From what I understand, if it were

C(0,t) - DcDx = 10

then,

pl  = cl - 10*D

Could you please confirm whether this is right?

[Torsten]

pl = -10*D;
ql = 1;

If you insert in the form used by pdepe (p+q*f=0), you get

-10*D + 1*D*Dcdx = 0,

thus

DcDx = 10.

[Deepa Maheshvare]

Thanks a lot for the clarification