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October 31, 2000, 00:15 
need help on solution to Stokes equations

#1 
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hi all,
I am a beginner in CDF. I want to solve 2D Stokes equations(i.e., steady Navier stokes equations without inertial terms for incompressible fluid) for complex porous microstructure where there exists regular/irregular shapes of solid particles. I need the velocity and pressure formulation of the equations rather than stream function approach. I have searched for codes written in Fortran for a while and one option was the commercial software ANSWERExpress, which is sold at a very low price for educational purposes. The manual says that it handles steady and transient laminar as well as turbulent problems. It explains the solution to the most general case, where the fluid is compressible and the flow is transient. The pressure correction term is given as a function of density correction multiplied by the partial derivative of pressure with respect to density correction term. In the manual this method is called "Density Equation Formulation of Continuity(DEFCON)" equation. It also relates the pressure correction to the gas law. But, when density is constant, there is no density correction and furthermore, the partial derivative term goes to infinity. So my question: how can I find a pressure correction term in this case? I can not understand how this approach works for steady flow with incompressible fluid. Maybe this is partially becuase I do not know different ways of solving NavierStokes as well as Stokes equations. I will really appeciate it, 1)if you refer me to any articles or books that clearly explain different approaches, 2) if you tell me a little bit about the approach taken by ANSWER software if you are familiar with it. 3) if you suggest me different fortran codes to solve laminar problems. thanks to all of you in advance 

October 31, 2000, 06:12 
Re: need help on solution to Stokes equations

#2 
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You might like to have a look at 2/E/FIX source code distributed by CHAM via its cfdSHOP. The code, sometimes called CHAMPION, was written in pre PHOENICS period and helped many, now prominent, CFD experts to get started.
If you went through the list of related reports ( it is very long though), you might be lucky to find something very similar to your project. Regards Sergei Zhubrin 

November 1, 2000, 16:15 
Re: need help on solution to Stokes equations

#3 
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thanks for your response. I think 2/E/FIX is a finite difference code. I am more interested in a code written by finite element or finite volume method, if I can find one. If I can not, that should be still a good choice. Do you know anybody who used it? I would like to ask some specific questions to make sure that this code will solve the type of problems that i want to work on. Thanks again for all the information.
best regards, yuksel onsoy 

November 2, 2000, 06:54 
Re: need help on solution to Stokes equations

#4 
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The 2/E/FIX is, indeed, a finite volume source code. It became publicly available since 1976 and was made freeofcharge for all the participants of many CFD seminars taken place at Imperial College organised by Heat Transfer Section,HTS, and later by Computational Fluid Dynamics Unit, CFDU.
One can try to trace its users, or rather their students, by reference to the HTS reports where some of them reported their simulations. I believe most of them are now with commercial codes built upon the Imperial College software sources which, nowadays, belong to the CFD history. PHOENICS and its shareware, for example, have inhereted from them veryuseropen structure of the solvers and underlying physical models. Regards Sergei Zhubrin 

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