Hi everyone,

I am a newbie in pressure-correction method (solution of Poisson type equation for pressure) and trying to develop a new CFD code in cylindrical coordinates and on non-staggered grids based on this method.

I had coded the algorithm, everything looks fine to me but there must be something wrong since the code explodes. Most of the books I come up with discusses the issue in cartesian coordinated and on staggered grids due to well-known reasons.

My question is, can anyone suggest any sources especially discussing the issue in terms of cylindrical coordinates(books etc.) which I can start with? Or are there any source codes which are publicly available that will serve for my purpose? I know it's a bit general but what might be the critical issues which I should pay special attention?

Thanx everyone in advance,

abilge

Check out Suhas Patankar's book.. It is one of the classical texts on this.

What solver are you using for solving the poisson equation? Have you tried FISHPACK? Ususally for non-staggered grid, the Rhie-Chow interpolation is used to avoid pressure-velocity decoupling.

Hi Sachin,

Thanx for your fast response first of all...

Correct me if I'm wrong but as far as I remember that book fully describes SIMPLE method for incompressible flows involving heat transfer and again in cartesian coordinates.I guess you are right, it is a classical text on the subject matter since every paper I come across cites that book.

Perhaps I was not clear with my question. My goal is to solve the pressure Poisson equation in cylindrical coordinates to obtain the pressure field. And while doing this I do not want to deal with staggered grids. So I believe what I want to do is different from SIMPLE algorithm. I know that this is doable by referring to a paper by Abdallah (1987). But in that paper things are still in cartesian coordinates.

Do I ask for too much Thanx for your time once again.

abilge

Hi agg,

I want to thank you too for your fast response.

Let me describe the situation once more for clarity:

I have obtained the pressure Poisson equation in cylindrical coordinates by taking the divergence of momentum equations and invoking equation of continuity for zero divergence condition. And I intend to use Neuman type boundary conditions except for the exit (we are talking about a laminar pipe flow where the exit is open to atmosphere so the exit boundary condition is Driechlecht). For the solution of the Pressure Poisson equation I use successive over relaxation (SOR) with a relaxation coefficient of 1.7.

Coming to your comment; No I have not heard about FISHPACK. What is it used for? And you've talked about "Rhie-Chow interpolation" to avoid velocity-pressure decoupling? Can you suggest any references for that? I believe this is what I'm looking for since I heard the most troublesome aspect of the subject at hand occurs while implementing the Neumann type boundary conditions. Perhaps what you have suggested might help..

Than you once again for your time..

abilge

Hi,

Have you tried under-relaxing? say alfa_p' = 0.6 (alfa_p<1). "SIMPLE" like algorithms usually require the pressure corrections to be under-relaxed. However,Energy equation may zip through with over-relaxing.

Hope this helps

Abhijit

Hi Abhijit,

Well as I mentioned previously, I tried over-relaxation upto now. Perhaps under-relaxation might help but since my eventual goal is to couple energy equation, this might cause problem as you told. However, it is worth trying I believe since energy equation is not present in the solution at the moment so I'll give it a try and let you know about the outcome.

Thanx a lot for your time...

abilge

Hi,

I forgot to mention, that one set of relaxation parameters (for u,v,w,p' & Temperature/Energy) in general will not work for all problems, you need to play with those. Relaxation parameters are very much problem dependent. If you use SIMPLE you may need to under-relax momentum equations as well (again its problem dependant). This is usually the case unless you use sophisticated algorithms (MG,Preconditioners....) Problems with large gradients in any of the primitive variables usually require under-relaxation.

If under-relaxing all the variables does'nt work, then it could be bugs in the code. To begin with you can try a very simple case of 2-D flow between fixed parallel plates.

Abhijit

Hi Abhijit ,

That seems like just the kind of information I'm looking for. As you might appreciate you may have to go through thousands of references just to come across such an information.

By the way I guess I am about the discover the bug you are talking about on a 2D laminar pipe problem. If I handle it then I may proceed with adding energy equation. Then I'll decide whether I should move on to more sophisticated algorithms such as multigrid methods or so because it seems like I'm gonna suffer from the slow rate of convergence.

I'll let you know..

Thanx once again for your time..

abilge

For FISHPACK (uses cyclic reduction technique): http://www.scd.ucar.edu/css/software/fishpack/

For MUDPACK (uses multigrid techniques): http://www.scd.ucar.edu/css/software/mudpack/

You can use the above solvers to compare results with the method you use now, so you know your implementation is correct. I have used Fishpack, it uses second-order discretization and is fast. You can also try Mudpack.

The Rhie-Chow interpolation is not just for the boundary, but in general to have the discretization of Pressure Poisson equation consistent with that of divergence and pressure gradient operator. You can find the refence in any standard CFD text book or search on google.

Hi agg,

Well I still cannot believe you sent me the links to source files I hope I can manage to incorporate these subprograms in my code. If I can it would be wonderful.

By the way I solved my previous problem (solution of cylindrical pressure Poisson equation on non-staggered grids). However, as you might guess, the code suffers from low rate of convergence since I do not use multigrid methods or so..Perhaps the source that you have pointed out may help me handle this issue.

In the mean time I looked for documents regarding to Rhie-Chow interpolation. Now I'm going over those..

Thanx for everything especially for your time..

abilge

Hi agg,

I just want to ask you something:

Suppose that I want to use the non-staggered version of FISHPACK to solve the Poisson equation for pressure and supplied the right-hand-side function to FISHPACK an d it produced a pressure field (and we don't know for sure whether this pressure field is the desired field or not). My question is: Do I have to compare the results produced by the consecutive calls of the FISHPACK and carry out an error analysis i.e. the global error is less than a certain value?

This might sound like a very nerdy question to you (I want to apologize in advance if it is) since I could not go into FISHPACK (I was busy fixing the bugs with my existing code, thanx GOD I've fixed it) but I could not find any sort of error definitions in the arguement list of the package. Your answer might help me plan things in advance before I jump into things.

I would like to thank you for everything once again. You were like a candle in my darkness by showing me an alternative way (seriously!).

abilge

No you do not have to check consequtive calls. What you can do is for the same right hand side, you can call Fishpack once and also your solver once and then check the two solutions. If there is a significant difference, it could be because of boundary conditions (if you use iterative technique and Fishpack uses direct methods) OR you have implemented Fishpack incorrectly in which case, you will have to use a right hand side for which you already know a solution as a check OR the implementation of your pressure solver is incorrect (but since you say that you have fixed the bugs, unlikely to be the case, but no harm in checking again right!)

OR

You can skip Fishpack altogether and just use your solver for a standard Laplace problem for which analytical solution exists. You will find such a problem in "Computational fluid dynamics" by T.J. Chung and more in "Conduction of heat in solids" by H.S. Carslaw and J.C. Jaeger