Constrained interpolation (remap) of divergence-free fields

A novel constrained interpolation algorithm for remapping of solenoidal face finite element vector fields is presented. The algorithm is based on explicit recovery, postprocessing and interpolation of a potential for the original vector field and a subsequent application of a curl operator to obtain the desired divergence-free finite element field on the new mesh. The use of interpolation instead of advection in the remap process offers valuable computational advantages. Old and new meshes are not required to have the same connectivity, nor to be close to each other. Slope limiting and upwinding, which can be sensitive to grid structure, are avoided and replaced by local optimization to control energy of the remapped field. The new method is validated using a suite of cycling remap problems on random and tensor product mesh sequences. A comparison with a local remapper based on a constrained transport advection algorithm is also included.