I solve multi-species, compressible Navier-Stokes equations on a 3D structured grid. I have obtained a solution on a given grid (let's say a relatively coarse one). I want now to refine my grid and interpolate my previous solution on my new grid before restarting my simulation. Currently, we have an interpolation tool that builds a k-d tree of the 2 grids and then can use 2 different methods to compute the values on the new grid:
- simple averaging
- inverse-distance-weighted (IDW)
- moving least squares (MLS)
I want to focus on accuracy because since I deal with large gradients, not capturing them correctly will generate waves when I restart my computation. I first tried simple averaging but the accuracy was not good enough.
I thought MLS method with polynomials of order 2 would give me reasonable results since it is supposed to be non-oscillatory. However, when I look at my interpolated field, I see local minima/maxima that overshoot values of my initial field. Does this mean the implementation of MLS in this program is not correct? Should I be careful with the size of my stencil and the order of the polynomials? Which other method would you recommend?
Thanks in advance !