Hello all,(adsbygoogle = window.adsbygoogle || []).push({});

This is my first post...

I am trying to make a code to numerically solve a problem, which is a heat conduction problem (temperature) in a moving slab (in y-z plane) with a source term in it:

A(dT/dy)=(d2T/dy2 + d2T/dz2) + B

dT/dy=0 at y=0, T=given at y=0, boundary conditions along y at z=0 and W are described by some simple functions. Say the width of the slab is W and the length is L.

I think this is called "convection (or advection)-diffusion" problem.

Because the way boundary conditions are given, to me (I don't know much about numerical methods), it looks like a "shooting method" can handle this problem. Or maybe the Crank-Nicolson method can be used, while taking y in this problem like t in a conventional C-N problem. Well, it seems like I cannot numerically solve this problem using these methods. The solution blows up.

Maybe I should use a method to handle a typical elliptic equation problem. But in this problem, one side is open so that I cannot specify the boundary condition at one end of y=L (I can specify both T and dT/dy at y=0, instead).

So here I am. I am stuck. Does anybody can give me some advices? In summary, my questions are:

(1) can a shooting method (like Runge-Kutta or whatever) be used to solve this kind of PDE problems?

(2) if I have to apply a method for a boundary value problem, how can I do to this problem that does not have a specified boundary condition at one end?

Thank you very much!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Numerical methods for solving convection-diffusion PDE

Can you offer guidance or do you also need help?

**Physics Forums | Science Articles, Homework Help, Discussion**