Combination of cartesian and cylindrical coordinate system
I have to solve a numerical problem namely how air is flowing first through a porous medium followed by streaming of the air coming out of the porous medium in a very narrow channel flowing to the ambient (journal porous air bearing).
This problem can be described with the use of two equations namely the Laplace equation describing the flow in the porous media, and the Reynolds equation describing the flow in the gap.
These equations must be solved both separately on an iterative manner until the pressure at the boundary between the porous media and the gap is equal to each other (continuity).
My question is: Can I use a cartesian coordinate system for solving the Reynolds equation (flow in the gap) and a cylindrical coordinate system for solving the Laplace equation (flow in the porous media) if I take care that the nodes where I calculate the pressure at the boundary between the gap and the porous media lie at the same place?
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