Discussion Forum

Dear Comsol Community,

as already described in the linked discussion (www.comsol.com/community/forums/general/thread/54351/) I want to study the steady flow in the gap between an air-hockey table and a levitating rectangular plate with a structured surface. Because I am not interested in the flow in the plate of the air-hockey table, I have tried to substitute the flow in porous media (Darcy’s law) with an equal boundary condition at the bottom of the gap (laminar flow, Navier-Stokes equations). It makes sense to me, to couple the local inlet velocity with the local static pressure at the inlet. Far away from the lateral outlet the inlet velocity will be very low (almost or equal zero), whereas near the outlet the inlet velocity will become maximal. Hence the boundary condition at the inlet is given by the expression , where denotes the local normal velocity, the local pressure, the dynamic viscosity, the permeability of the porous plate, the pressure at the inlet of the porous plate and the thickness of the porous plate. The expression can be interpreted as a hydraulic resistance . Initial runs of my simulation yields strange results. The lower boundary of the gap seemed to be a mass source. The fluid entered and leaved the domain at the same place and the evaluation of mass fluxes showed that the conservation of mass was heavily violated. To avoid this problem I have added the nojac operator to the boundary condition . On the one hand this seems to solve the problem with conservation of mass one the other hand the speed of convergence gets worse, especially if the aspect ratio becomes very low. Sometimes the chosen solvers even fails to find a solution (especially in three dimensional models). I have already found out, that the double dogleg nonlinear solver seems to have less problems with convergence compared to the automatic (highly nonlinear) newton algorithm.
Form a mathematical point of view this boundary condition seems to be correct, however Comsol has some trouble with handling it. Do you have any experience using similar boundary conditions?
Do you have any advices how to improve the speed of convergence or my model at all? Is it possible to get rid of this numerical unstable boundary condition and replace it with another equal but more stable one. I have also tried to reinterpret the inlet velocity boundary condition as inlet pressure boundary condition
This works perfectly in 2D, but in 3D I don’t get any solution if the aspect ratio is very low.

For those of you, who are interested in this problem, I will upload a model tomorrow.

Thank you very much in advance.
Best regards
Maximilian

PS. I know that my boundary conditions is not realistic regarding the tangential velocity at the boundary. Nevertheless I want to use it ;-) I have already ruled out problems with the mesh by assuming the inlet velocity to be constant or a function of space.