## Solving advection diffusion pde

Asked by Deepa Maheshvare

### Deepa Maheshvare (view profile)

on 25 Dec 2018
Latest activity Commented on by Deepa Maheshvare

### Deepa Maheshvare (view profile)

on 2 Jan 2019 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

### Deepa Maheshvare (view profile)

on 27 Dec 2018
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

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Answer by Bill Greene

### Bill Greene (view profile)

on 27 Dec 2018

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

### Deepa Maheshvare (view profile)

on 29 Dec 2018
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

### Torsten (view profile)

on 2 Jan 2019
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

### Deepa Maheshvare (view profile)

on 2 Jan 2019
Thanks a lot for the clarification