I have read two book,one is "Riemann solvers and numerical methods for fluid dynamics" wrote by F.toro,another is "Finite Volume Methods for Hyperbolic Problems" wrote by J.leveque. These book are mainle concerned on hyperbolic eqution. I want to use these method to Navier-stokes eqution,how can i solve with viscous? could you tell me some book about full discussion of these issues?

Hi,

I think, u can use the book from Malalasekera for a basic introduction on how to solve the NS equations. For an advanced approach, the Ferziger book is better...

In those books, u will find how to solve the NS equations with not so high-resolution schemes...

For higher resolutions, like an spectral solver, I think the FEM method is better.

And I think also that the NS equations must be solved by an eliptic solver not an Hyperbolic, due to the nature of the fisics involved, m I wrong???

Good luck...

The NS equations for viscous fluid flow are parabolic problems. I suggest you don't use hyperbolic approach for these kind of problems. It's my opinion to use the correct discretization form which may differ depending from the kind of problem. Maybe useful to read paper about the problem you want solve. I used, and sometimes use, the Tannahill - Anderson - Pletcher Computational Fluid Mechanics and Heat Transfer book during my studies and my work. I think it's a good reference point for cfd analysis. Bye Salvatore

The focus of the books you mentioned is on hyperbolic problems because the advective portion of the NS equations is hyperbolic. The ideas can be carried over directly to the solution of the Euler equations (which are hyperbolic) by applying the high-resolution discretizations to the advective terms. To include the viscous terms, use a central difference approach (structured grids) or use an appropriate approximation to the viscous terms on unstructured grids. This is a fairly standard procedure in constructing a CFD solver.

The method you mentioned is motivated,and i wang to know the detail of implement this solver to practice problem? Ask for some book or paper where this method has introduced or used?

Thanks Could you give some code about eliptic solver on NS equations?

Any decent entry-level CFD text will typically break the algorithm development into two pieces - one piece for the advection (which is where the Riemann-type solvers come into play) and one piece for the diffusive flux. Look at the texts by Anderson, Tannehill, and Pletcher, or Ferziger and Peric, or Hoffman and Chiang, or Hirsch.

Hi, if u look in the net, u will find some....

The code I'm using is based on the OPENFoam... it is a very good starting point....

If any problem, plz ask...

It is very hard to understand OpenFOAM, maybe for me.Can you offer some code writed by fortran, solve compressible NS equation