Assuming there exist two 2D grids on the same domain, one of them is a cartesian one while the other is curvilinear (body fitted regular grid, with curved coordinate lines).
I am looking for a way to transfer values (interpolate) between these grids. Assuming the body fitted grid is given in the form of coordinates of the cell centers in the cartesian system doing the interpolation from the cartesian to the body fitted grid is relatively easy, as simple bicubic etc. interpolation can be used on the cell center coordinates to find the corresponding cartesian coordinates and get the values from the grid with these.
On the other hand for the other direction, body fitted to cartesian, this cannot be achieved so easily, as it would essentially require the inversion of the body fitted to cartesian diffeomorphism (mapping).
I was wondering if someone may have some suggestions for this problem. The numerical inversion of the mapping can be carried out, however I am a little worried about the compound effect of the inaccuracies during this process with all the interpolation involved.