Hi, I have yet problems with my SIMPLER. I am testing lid driven cavity for collocated grid and the residuals for velocities are not going under certain values (10E-4 for example). I am solving a pressure correction and a pressure equation. What about Rhie Chow Interpolation in these equations? I have this only in the pressure correction method, but I do not know what I have to do in the pressure equation?! Can anybody help or has anybody a working SIMPLER routine for collocated grids!

Thank you very much!

Your answer is given in Dr. Hsu's Thesis (The academic advisor is prof. Patanker). "A Curvilinear-Coordinate for Momentum, Heat and Mass Transfer in Domains of Irregular Geometry' by Chia-Fu Hsu, 1981, Ph.D Thesis, University of Minnesota. The source code is also given in the thesis. I read that thesis ten years ago and I do not remember the details.

Write down the momentuntum equations for the cell-face velocities, then you have the momentum equation expressed in terms of the psedo-velocity components for cell-face velocities and the pressure term. Then, you get the psedo-velocity components for cell-face velocities by the interpolation of the pseudo velocities in the neighbouring cell-centerted points. So you should calculate the pseudo velocity components at the cell-centered locations before interpolation. Take care of under-relaxation factors in the momentum equation. Put that momentum equation in the continuity equation, then you have pressure equation. It is that simple.

I do not know why you use SIMPLER instead of SIMPLE(with optimal relaxation facor ,alpa-p=1.-alpa-u, where alpa is underrelaxation factor) or SIMPLEC. The collocate method is suited for SIMPLE or SIMPLEC.

Good Luck

Halim Choi

Dear Michael and Halim,

The thesis from Dr. Hsu's is a very good reference if you want to read the theory, and implementation. At one point in the early 90's, I also had access to the source code, and I noticed that there were certain inconsistencies. Even for a simple problem as 1-D pure conduction, it will produce wiggles in the solution near skewed control volumes for non-orthogonal meshes; however, for orthogonal meshes it worked just fine.. There is more in there than just the SIMPLER algorithm, but also an extension of an interpolation scheme based on piecewise splines that showed promise in a previous thesis by Dr. L Varejao (also Dr. Patankar's student)..

Why to use SIMPLER instead than SIMPLE/SIMPLEC? SIMPLER is much more robust than either of them. However, when the mesh scale is reduced (finer meshes), it seems to show some slow down in convergence rates.

Try to get a hand on the (from a library since it is not cheap)

Handbook of Numerical Heat Transfer W. J. Minkowycz, E. M. Sparrow, G. E. Schneider, R. H. Pletcher ISBN: 0-471-83093-3

I do not recall the chapter, but there is mention of the SIMPLE X (yes with an X), a modified version of SIMPLE which converges much better than SIMPLE/SIMPLEC and even SIMPLER for finer meshes (at least that is what I observed).. The reference is by the same authors/creators of SIMPLEC..

Good luck, Opaque..

Dear Michael,

I think you will find the following website interesting:

http://webfea-lb.fea.aub.edu.lb/fea/...blications.htm

Check the publication about a Unified Formulation of the Segregated Class...

You may also ask Dr. Darwish for some guidance..

Good luck, Opaque.

The SIMPLER algorithm solves pressure equation during the solution process and in a nonorthogonal grid situation the pressure equation involves nonorthogonal pressure terms that make the scheme messy. To avoid this problem Professor Patankar group (Dr. Karki, Dr. Hsu) used the covariant velocity components as cell face velocities. But in this case you have additional mass source terms in the continuity equation that should be obtained by interpolation of neighbouring velocity components and make coververgence very difficult in a strongly nonorthogonal grid situation (grid angle less than 30 degree). When we consider an unstructured grid situation the implementation of SIMPLER algorithm is very messy and nobody used it. In my experience the SIMPLEC algorithm is as good as SIMPLER algorithm in convergence. Then, why you use SIMPLER algorithm?

Hi Halim!

My problem is not to get a very fast algorithm, I already implented SIMPLEC and it works very fine. I want to learn how to handle a pressure equation instead of a pressure correction equation. In a pressure correction equation I have have real massfluxes on the right hand side and I can easily get expressions for Rhie and Chow Corrections. But in a pressure equation I have on the right hand side massfluxes from pseudo velocities and I do not know how to handle them in a collocated arrangement, I see only that my SIMPLER does not want to converge (it also does not diverge!). That's the point I want to understand and learn.

Regards, Michael!

(1) Define and calculate the pseudo velocities at cell-center and store it.

(2) Calculate pseudo velocities at the cell-face through a linear interpolation of pseudo velocities at neighbouring cell-centered locations (similar to Rhie-Chow interpolation)

(3) Caluate the source term of pressure equation using the pseudo velocities at cell-faces (obtained from (2))

(4) Calculate the pressure equation.

If you still do not understand what I am talking, give me your email address. My email address is skchoi@kaeri.re.kr