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Old   August 29, 2005, 04:42
Default FISHPACK F90 package for Navier-Stokes solvers
  #1
Ahmet Bilge Uygur
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Hi all, I am trying to implement FISHPACK F90 package to my existing code for the solution of pressure Poisson equation instead of the classical iterative technique.

Does anyone know any successfull implementation? Are there any critical issues which I should pay special attention? Any resource might be helpful (paper, book etc.)

Thanks in advance,

Ahmet
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Old   August 29, 2005, 12:35
Default Re: FISHPACK F90 package for Navier-Stokes solvers
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agg
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Have you looked at the examples they have? Can you describe in more detail where you are stuck?
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Old   August 30, 2005, 04:18
Default Re: FISHPACK F90 package for Navier-Stokes solvers
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Ahmet Bilge Uygur
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Hi agg,

By the way I checked my message archive and I realized that this is not the first time you're helping me As far as I remember you adviced me to look for the FISHPACK package. From that moment on I did quite a lot of things. I would like thank you for everything before I start

The situation is as follows:

I downloaded the FISHPACK F90 package and carefully went over the relevant examples and tutorials. As a starting point I attempted to solve a simple Poisson type equation on cartesian coordinates and validated the solution I obtained with FISHPACK against the classical iterative solution. Having seen that I obtained successful results I proceeded with Navier-Stokes solution.

At this point a little info on the CFD code I am currently working on: The code is a transient code based Method of Lines (MOL) (an efficient semi-discrete technique for the solution of PDEs). In MOL the spatial derivatives are evaluated using high order approximations by employing readily available discretization packages such as 4th order lagrange interpolation polynomials. Then after spatial discretization, you obtain a set of ODEs in time and you integrate these ODEs using a powerful ODE solver such as LSODES. My overall scheme is in a way similar to PISO (pressure implicit with splitting operators), I predict velocities then correct it once, then predcit temperatures, correct temperatures etc..

I implemented the FISHPACK package to my CFD code. I first tested the code on a isothermal problem and obtained excellent results. While doing this, I computed the Poisson source term necessary for FISHPACK using the same discretization packages mentioned above.

Then I tested my code on a non-isothermal (walls of the pipe is heated) turbulent (Re=4200) test case. I obtained meaningful results. However, I realized the followings:

*The magnitude of the pressures computed by FISHPACK are hihgly sensitive to grid resolution. *At the first 4 time steps I observe negative pressure values (which is not reasonable)then after the 5th time step reasonable pressures are obtained then code starts to produce somewhat nice results till the steady state. *Although the results are reasonable, they are not as good as I want them to be. (10% relative error)

I do know that success of a CFD code depends on many factor, so many that we cannot list them all here.

The reason I posted this message was, to learn if someone else who had previously worked with FISHPACK encountered similar problems. More specifically;

*Can you comment on my discretization scheme? Is it okey to use such a package for discretization while computing the Poisson source term? *While choosing the grid resolutions, should I establish it in such a way that delta r= delta z?

You told me describe in detail and perhaps this message was too much in detail Sorry if I took a lot from your precious time and lots of thanks in advance..

Ahmet

PS. You are always a helping hand After your previous message the whole course of my study has changed dramatically. Thanks one more time

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Old   September 1, 2005, 03:52
Default Re: FISHPACK F90 package for Navier-Stokes solvers
  #4
Ahmet Bilge Uygur
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Hi agg,

I just recieved an e-mail today that you have posted a message in response to my previous, rather long, e-mail. However when I click the link I see that the link is dead. If possible can you post your reply again?

Thanks in advance,

Ahmet
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Old   September 2, 2005, 11:10
Default Re: FISHPACK F90 package for Navier-Stokes solvers
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agg
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Hi,

I think my message was one of those accidentally deleted by the admin. Here are my thoughts.

1) Since you were able to obtain good solutions for the non-isothermal case, the problem COULD be somewhere else and not the Poisson solver (bouyancy term in momentum equations, just a guess)

2) Fishpack is a second order finite difference solver. Ideally, you should not use the 4th order scheme to compute the source term of your Poisson equation. Remember, d2P is divergence of the pressure gradient. Hence, the divergence and pressure gradient operator should be consistent. You could still use the 4th order Lagrangian scheme for other variables. I had problems with stability for my finite difference solutions and so I moved pressure to center of the cell. Your solution however, seems stable, but the inconsistency in the differentiation could be responsible for the inaccuracies that you are noticing.

Here are some references that will be helpful before you decide to make any changes to your code

1) "Numerical heat transfer and fluid flow", Patankar (chapter 6)

2)"Numerical study of the turbulent flow past an airfoil with trailing edge separation", Rhie and Chow, AIAA Journal, Vol. 21, No. 11, p. 1525-1532 (1983)

3)"Numerical solutions for the pressure Poisson equation with Neumann boundary conditions using a non-staggered grid, I", Abdallah, JCP (70), p. 182-192 (1987)

4)"The discrete continuity equation in primitive variable solutions of incompressible flow", Sotiropoulos and Abdallah, JCP (95), p. 212-227 (1991)

5)"Alternate formulations for the pressure equation Laplacian on a collocated grid for solving the unsteady incompressible Navier-Stokes equations", Danesh Tafti, JCP(116), p. 143-153 (1995)

Good Luck!
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