MATLAB Central Newsreader - Convective diffusion equation in 2D

Convective diffusion equation in 2D

dantimatter — Fri, 03 Aug 2007 14:57:53 -0400

Hello all,

I'm trying to find a nice and neat way to numerically solve the
convective diffusion equation

da/dt = D (d^2/dx^2 + d^2/dy^2) a - v da/dx

where a is the concentration of my solute, D is the diffusion
constant, and v is the surrounding fluid velocity in the x direction.
I thought that there was a small chance that maybe someone else here
has attempted something similar.
Is it even possible to solve this equation? As always, any suggestions
would be much appreciated.

Cheers,
Dan

Re: Convective diffusion equation in 2D

Mukesh V — Fri, 14 Dec 2007 16:52:00 -0500

Re: Convective diffusion equation in 2D

Bruno Luong — Fri, 14 Dec 2007 17:47:35 -0500

I just want to share few knowledge on solving this type of
equation:

- It's preferable to discretize time by implicite scheme for
stability, at least for the laplacian (diffusion) term.

- The convection term needs to be discretized by "up-wind"
scheme, that warrants also the stability and ensures the
solution to satisfy entropy condition. The up-wind is more
tricky to implement in 2D than in 1D.

Good luck,

Bruno

Re: Convective diffusion equation in 2D

Thomas Clark — Mon, 17 Dec 2007 23:50:34 -0500

dantimatter <dantimatter@gmail.com> wrote in message
<1186153073.038814.223160@d30g2000prg.googlegroups.com>...
>
> Hello all,
>
> I'm trying to find a nice and neat way to numerically
solve the
> convective diffusion equation
>
> da/dt = D (d^2/dx^2 + d^2/dy^2) a - v da/dx
>
> where a is the concentration of my solute, D is the diffusion
> constant, and v is the surrounding fluid velocity in the x
direction.
> I thought that there was a small chance that maybe someone
else here
> has attempted something similar.
> Is it even possible to solve this equation? As always, any
suggestions
> would be much appreciated.
>
> Cheers,
> Dan
>

My friend, you have just opened the third biggest can of
worms in classical physics (IMHO!).

Check the following link out. It's not matlab per-se, but
there are matlab import-export routines for the files. If
you know C++ (or are relatively fearless / have a bit of
time on your hands), it's a very efficient solver for pretty
much any PD Equation... I think one of the examples might
include a convection-diffusion setup. To give you an idea, I
didn't know C++, and it took me about a week to get up to
speed with this solver, using a C++ textbook as a guide.

Please note that it's a pretty specialised solver (spectral
domain, for efficiency) and there are a lot of similar
things out there on the web. Many of them will be simpler to
implement, although beware there is a minefield of badly
written code, too!

http://wissrech.ins.uni-bonn.de/research/projects/AWFD/

If you need some help setting it up, I may be able to offer
advice (or at least some really heavily commented code that
I've developed). Fire off an email to the address shown
(removing spam labels, of course)

Good luck!

Tom Clark

Re: Convective diffusion equation in 2D

Thomas Clark — Mon, 17 Dec 2007 23:50:40 -0500

Re: Convective diffusion equation in 2D

Thomas Clark — Mon, 17 Dec 2007 23:55:16 -0500

dantimatter <dantimatter@gmail.com> wrote in message
<1186153073.038814.223160@d30g2000prg.googlegroups.com>...
>
> Hello all,
>
> I'm trying to find a nice and neat way to numerically
solve the
> convective diffusion equation
>
> da/dt = D (d^2/dx^2 + d^2/dy^2) a - v da/dx
>
> where a is the concentration of my solute, D is the diffusion
> constant, and v is the surrounding fluid velocity in the x
direction.
> I thought that there was a small chance that maybe someone
else here
> has attempted something similar.
> Is it even possible to solve this equation? As always, any
suggestions
> would be much appreciated.
>
> Cheers,
> Dan
>

My friend, you have just opened the fourth biggest can of
worms in classical physics (IMHO!).

Check the following link out. It's not matlab per-se, but
there are matlab import-export routines for the files. If
you know C++ (or are relatively fearless / have a bit of
time on your hands), it's a very efficient solver for pretty
much any PD Equation... I think one of the examples might
include a convection-diffusion setup. To give you an idea, I
didn't know C++, and it took me about a week to get up to
speed with this solver, using a C++ textbook as a guide.

Please note that it's a pretty specialised solver (spectral
domain, for efficiency) and there are a lot of similar
things out there on the web. Many of them will be simpler to
implement, although beware there is a minefield of badly
written code, too!

http://wissrech.ins.uni-bonn.de/research/projects/AWFD/

If you need some help setting it up, I may be able to offer
advice (or at least some really heavily commented code that
I've developed). Fire off an email to the address shown
(removing spam labels, of course)

Good luck!

Tom Clark

Re: Convective diffusion equation in 2D

sumayyah — Tue, 18 Dec 2007 01:34:25 -0500

Hi dan

im just see this forum.
im also will use this equation. Someone advice me to use
Fortran to run this kind of equation. Now im still trying
to solve this equation.
have u solve this equation? now, im still use 1D equation,
after this i will use 2D. may i share experience with u?

thank you
Regards

Re: Convective diffusion equation in 2D

Vishal Nandigana — Sun, 28 Sep 2008 22:36:02 -0400

Hi

I am solving a 2D convection diffusion equation using Finite Volume method by writing my own codes. Further may I know whether there are any source codes available to solve these equations. I saw this link

http://wissrech.ins.uni-bonn.de/research/projects/AWFD/UsersGuide/AWFD/index.html

and found that its only for finite difference schemes. May I know where we can get source codes for these equations using Finite volume methods. (Either C, C++ or Matlab language codes(Matlab will have memory problem though)).

Kindly do the needful help.

With Regards

Vishal