Conservative interpolation between unstructured meshes via supermesh construction

Mesh adaptivity on unstructured meshes is a proven and popular tool for reducing the computational cost of numerical simulations. Unstructured meshes are often preferred in mesh adaptivity as they allow for greater geometric flexibility and arbitrary anisotropy in resolving simulation features. However, such mesh adaptivity suffers from a significant drawback: the interpolation errors caused by interpolating from the old mesh to the new mesh typically destroys conservation of quantities important to the physical accuracy of the simulation (e.g., density, volume fraction, tracer concentration, etc.). This work presents several globally conservative interpolation operators between general unstructured meshes via the construction of an intermediate supermesh. The construction of the supermesh is performed by transforming the problem to the input to a constrained meshing problem. The performance of the conservative interpolation operators are compared against interpolation using the underlying basis functions.