What is the effective to compute full NS equation
I am seeking effective methods to solve viscous compressible NS equation, any comments is welcome.

Re: What is the effective to compute full NS equation
(1). There are cfd books on various numerical methods to solve NavierStokes equations. (2). You can visit the books online section in the Resources of this Forum. If you are interested in commercial cfd codes, it is a good idea to visit the vendor's web sites.

Re: What is the effective to compute full NS equation
Try FiniteVolume based approach.
You can use upwind schemes for inviscid terms and centraldifference approach for viscous terms. For viscous computations Roe and Osher's fluxdifference splitting schemes are recommended. Assuming that you are using structured grid, you can obtain higherorder accuracy using MUSCL formulation. For more details you can refer to the following: The Journal of Computational Physics, Computers & Fluids, AIAA Journal, VKILecture series and AIAA Papers. Jawahar 
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