# Combination of cartesian and cylindrical coordinate system

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 November 30, 2011, 16:32 Combination of cartesian and cylindrical coordinate system #1 New Member   Join Date: Jul 2010 Posts: 10 Rep Power: 15 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?

November 30, 2011, 21:07
#2
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Arjun
Join Date: Mar 2009
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Quote:
 Originally Posted by Hermano 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?
Yes. I did this for pressure poisson equation. In fact you can exploit direct solvers to efficiently do it.