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Solutions to PDEs over irregular domains can be computed using the finite difference method by the introduction of so called body fitted coordinate systems where the coordinate lines are aligned to the domain boundary. The benefit of the idea is that the finite difference method can be applied directly to the problem in a new coordinate system (with certain modifications regarding the computation of the derivatives).

Body fitted coordinate system

As these modifications seem ridiculously complicated for practical consideration ( p. 18) I am looking for ways to make the problem easier by having a less generic coordinate representation.

My question is if using orthogonal coordinate systems has any advantages over a generic 2D curvilinear coordinate system (one to one mapping)? Orthogonal coordinate systems can be generated for a specific domain based on the Scwarz-Christoffel mapping (conformal mapping), what I would be interested in is if this approach would have any practical benefits, i.e. if orthogonality can somehow be exploited for this problem?

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