# Convection-Diffusion Test (Problems) Matrices

The convection-diffusion equation is of the form

-[Uxx + Uyy + Re( p(x,y)Ux + q(x,y)Uy )] = f(x,y).

Test Problem 1 (no recirculation).

• p(x,y) = Re (2y-1)(1-x^{2});
• q(x,y) = Re 2xy(y-1);
• u(x,y) = sin($\pi$ x) + sin(13$\pi$x) + sin($\pi$y) + sin(13$\pi$y).

Test Problem 2 (recirculation).

• p(x,y) = Re 4 x(x-1)(1-2y);
• q(x,y) = Re -4 y(y-1)(1-2x);
• u(x,y) = sin($\pi$ x) + cos(3$\pi$y) + exp(xy).

Test Problem 3 (recirculation).

• p(x,y) = Re sin(2$\pi$x)cos(2$\pi$y);
• q(x,y) = -Re cos(2$\pi$x)sin(2$\pi$y);
• u(x,y) = exp(xy) + exp(-xy).

Here are the Fortran codes for

I do not plan to have too many similar test problems to confuse users, but if you can convince me that a particular test problem is better than the one that I put in here, I would be happy to make a change. However, a test problem with discontinuities may be added.
Here are some relavent references.

For problems and suggestions, send e-mail to: jzhang@cs.uky.edu.

DISCLAIMER:
• This page was created by Jun Zhang as a voluntary service to the community of iterative method researchers and practioners. This software package comes with no warranty. The author is not liable for any loss/damage or inconvenience caused in the use of this software or any modification thereof. You use it at your own risk.
• Matrices and their information were generated using Sparskit Package.