High order accurate conservative remapping scheme on polygonal meshes using a posteriori MOOD limiting

In this article we present a high order accurate 2D conservative remapping method for a general polygonal mesh. This method conservatively projects piecewise constant data from an old mesh onto a possibly uncorrelated new one. First an arbitrary (high) accuracy polynomial reconstruction operator is built. Then, the exact intersection between the old and new mesh is constructed, leading to a submesh of old subcells paving any new cell. Last, a high order accurate quadrature rule is designed to integrate the arbitrary high order accurate polynomials on the subcells to get a final new piecewise constant cell average on any new cell. The technique is limited a posteriori in such a way that effective high accuracy is maintained on smooth solutions while an essentially non-oscillatory behavior is observed on an irregular solution. Moreover, intrinsic physical properties of the system of variables such as positivity can be ensured. Numerical results assess that such a method is effective on problems for scalar remapping (smooth and discontinuous). We have also considered the remapping of multiple coupled quantities, such as mass, momentum and energy. The results confirm that this remap method is efficient in situations containing irregular/discontinuous profiles and smooth parts, for which some physical admissible constraints such as positivity must be ensured.