need help on solution to Stokes equations

Yuksel Onsoy

hi all,

I am a beginner in CDF. I want to solve 2-D 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 ANSWER-Express, 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 Navier-Stokes 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