I have a finite difference model for solving the Reynolds equation. This model can only work with a uniform grid. But I also want to use this model for non-uniform grids. Therefore I will use a grid mapping technique based on the Jacobian matrix. I know how this is done for the first spatial derivative (with the inverse of the Jacobian) but there are also second order spatial derivatives in my equation. How is this done for the second order derivatives (central difference formula)? Also with the Jacobian matrix? How does the Jacobian Matrix then look likes?
I think you should be able to find what you're looking for in here:
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