Hi: I have noted that many people write the discretized equain in a matrix form when solving the compressible flow, while we do not do in this way when solving the incompressbile flow! so what is the difference between the two methods!

Hi,

Well, the matrix form originates whether ur solving it implicitly or not. As per my observation, for incompressible flows, owing to the absence of pressure update (apart from pseudo compressibility methods) we solve for pressure : Del^2 P = F(Del dot U).. so this discretization results in a system of equations ..a sparse matrix system.

Also the presence of viscous terms, we cannot afford to use explicit discretization..So again implicit

For compressible flows explicit discretization is very easy and straightforward, the problem being stability. In this case u choose an implicit method, u get the matrix form again.

-Dominic

I am really confused about how to assemble all of the points to a matrix, do you have any good instruction! regards

Hi,

Yes, when its 2D or 3D the matrix is huge and its banded.

Here is a ref which may help you, it has what you want :

Computational fluid dynamics for engineers (2 volumes) Hoffmann, Klaus A.

Publisher: Engineering Education System, Pub date: 1993 ISBN: 0962373176

Regards, Dominic

Thank you again! then how to solve the sparse matrix, i want to use the direct method , do yo know is there some free package for the direct gaussian elimination ! regards

Hi,

May be can Try : LAPACK http://www.netlib.org/lapack/

or PETSc : http://www-unix.mcs.anl.gov/petsc/petsc-as/.. they are free

regards,

Dominic