Hi all,

I have written a CFD code for simulating transient laminar flow in a cylindrical cavity. Since the model assumes temperature-dependent viscosity, I discretized the tensor-form of Navier-Stokes equations using Finite Volume. My velocity components are (u along radial direction (r), v along the azimuthal direction (theta) and w along axis(z)). A staggered MAC grid was used.

When updating v nearest to the pole, I needed to compute a component of the stress tensor (tau_r_theta) at the pole. Therefore, I used equation (37) of the Morinishi, Vasilyev and Ogi paper (Fully Conservative ....). My problem is that when I used the central difference scheme, the computed values did not converge. However, when I tried a forward/backward difference scheme, the computations do converge.

I would like to know if anyone of you has come across a similar situation before. I would like to have a reference that would confirm the scheme I am using is correct in this particular situation.

Are you solving an axisymmetric problem (rotating flow) or a full three-dimensional problem? If a full 3-d, the conditions on the axis are a continuing problem. You might try searching the archives for cfd-online for previous discussion. If axisymmetric, help with that should show up as well when you search.

To generalize (there will be other opinions on this), the axisymmetric problem is not too hard to handle. The general 3-d problem is often treated by special 'fixes' in the cylindrical system. The preferred system (I think) with commercial codes is to use Cartesian (!) coordinates and use a block-structured mesh with 5 blocks of generalized (distorted) bricks to mesh the problem.

It is common to find that centered difference schemes (for the advection terms) can lead to instability - see for instance C. W. Hirt's "Heuristic Stability Theory" in JCP in the late 1960's.

Thank you for the reply. In fact, I am modeling a full 3D flow in cyln coords. For the advective part I used a hybrid centered-upwind scheme. It works pretty well without instablity. However, the tensor terms that I am refering to are found in the diffusive part of the N-S equations. I tried to browse the CFD-online archive but none of the discussions provided a solution to my problem(s).

Maybe I can send you a pdf of what I am trying to solve and the problems I am facing...

I'll be glad to look. Don't know if I can help.

I think all you have to do is click <send e-mail> next to my name and attach your pdf.

Thank you for your kind help.

I will send you the doc ASAP.