My present work involves developing a 2D thermal solver for an ablating material using finite volume methods. Upon reaching ablation temperature, the material will ablate and changes its geometry with every time instant. i.e., the cell centers of the mesh will change with time. After performing the surface recession, I need to interpolate the material properties to the new geometry cell centers from the old cell center values.

For a 2D regular geometry, I'm able to perform the bilinear interpolation. But for an irregular geometry, interpolation becomes a bit difficult. So far I have tried the RBF method, Shepard's method. But I face some numerical errors. Are there any better ways to perform 2D interpolation in a moving mesh for an irregular geometry?

Thanks & Regards,

Ahilan Appar