Combination of cartesian and cylindrical coordinate system

AI Thread Summary
The discussion revolves around solving a numerical problem involving air flow through a porous medium and a narrow channel. The Laplace equation is used for the porous media, while the Reynolds equation is applied to the flow in the gap. The key question is whether a Cartesian coordinate system can be used for the Reynolds equation and a cylindrical coordinate system for the Laplace equation, provided that the boundary nodes for pressure calculations are aligned. The geometry and dimensions of the system, along with the type of bearing involved, are also critical points of inquiry. Understanding the coordinate system compatibility is essential for accurately modeling the flow dynamics in this scenario.
hermano
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Hi,

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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