Hello !!

Presently I involved in 2D Laminar Viscous Compressible flow computations. I validated the inviscid part of the code by several compressible benchmark problems. I am using Unstructured mesh FVM (cell centered) for my computations...

I am facing some serious problems for viscous computations..For external flow pbms (Airfoil).. I am making farfield boundary circle 40 chords away from the airfoil.. I am using Green-Gauss theorem for face gradient calculation. 1. Convergence Limiting problem.. While running the code.. I am facing Negative Pressure in a single control volume(not the same element always).. then convergence stops.. 2. For Flat plate case. i couldnt get exact no-slip (u!=0... u=0.02). i am using 0.01 size elements near flatplate.. 3. which is best? either FEM or FVM approach to calculate the face gradient for viscous part? and Why the CFD peoples are moving towards FEM for viscous part?

Please tell your views, good face gradient calculation approach, and about FEM for CFD? Thanks in Advance Yousuf

Dear Mohammad,

If your code has been validated succesfully for the inviscid part, the failure of the code can be attributed to the viscous part. The following are my comments

1. In case of flat plate, the exact no-slip will never be obtained, in the sense that if you are looking at the cell away from the boundary and you have imposed the no-slip condition at the boundary. Away from the no-slip boundary where it is the case that u=v=0, exactly, for any point infinitesimally away there would definitely exist an infinitesimmaly small velocity. Have you been able to validate the flat plate case ? This would be one of the simplest problems to take up.

2. You could try your problem with a circular cylinder at M=0.1-0.2 and Re=40 , instead of an airfoil, although strictly there should be no difference in the performance of the code in either cases. The far field boundary is not an issue, as long as it is 10-12 chords (40 is too large, but good if you are using a freestream BC on the boundary, so that the Cl, Cd are grid-independent). Also check your farfield BC.

Are you using a first order scheme or a reconstruction procedure? Also, check the time step if you are using an explicit scheme. Even if the scheme is implicit, try reducing the CFL.

3. FEM and FVM are jsut discretisation procedures. The popularity of FVM in CFD is just because it was designed that way, and has the interesting property of conservation bulit into it by default. Visocus flux discretisation is truly an issue in itself, Green-Gauss procedure however should do the job, as it is reportedly robust inspite of being inconsistent on arbitrary polygonal meshes like the one you use.

Hope this helps Regards

Ganesh

Dear Mohammad, I am agree with ganesh, you should first to validate your code for the invicid part. After that, you can start to worry about the viscous part.

Regarding FEM vs. FVM, these is a common discussion. In my view, most people in CFD are using FVM due to the embedded mass conservation property. On the other hand, people using FEM are more worry in finding the solution of the problem. A good solution will garanty mass conservation with a given accuracy. Depending on your problem or expectations, you can choose between FEM or FVM. However, to choose FVM due to its forced "conservative" property should not be the main argument.