I'm trying to develop a code to solve the stream function-vorticity equations using the Finite Element Method in order to simulate a 2D incompressible flow problem. I was wondering what the pros and cons are, whether coupling a turbulence model is possible, whether formulating the boundary conditions may face difficulty and whether the evaluation of the pressure field is flawed possibly due to decoupling of the pressure variable from the governing equations. Note an accurate evaluation of the pressure field is particularly important for my case of study.
I very much appreciate helping me out.
You may be asking the wrong question here. Why do you say the flow is "incompressible"? Most flows are incompressible, even if the density varies. Technically, incompressible means low Mach number, not constant density. If your flow has significant viscous effects, the stream function-vorticity method may be inappropriate. Why do you want to use the FEM? Why not the FDM or FVM? Why not use one of the popular free codes, like OpenFOAM? If you're concerned with turbulence models, you may not be approaching the problem correctly. There are many posts on RG regarding fluid flow modeling so there are others working on similar problems. I suggest you delve deeper into this subject before continuing.
Hi Sourangshu Ghosh ,
I suspect you will find much of what you are looking for in this already existing RG Question:
https://www.researchgate.net/post/What_are_the_pros_and_cons_of_basing_the_simulation_of_an_incompressible_flow_problem_on_the_stream_function-vorticity_formulation
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