Fast optimization-based conservative remap of scalar fields through aggregate mass transfer

Abstract

We develop a fast, efficient and accurate optimization-based algorithm for the high-order conservative and local-bound preserving remap (constrained interpolation) of a scalar conserved quantity between two close meshes with the same connectivity. The new formulation is as robust and accurate as the flux-variable flux-target optimization-based remap (FVFT-OBR) [1,2] yet has the computational efficiency of an explicit remapper. The coupled system of linear inequality constraints, resulting from the flux form of remap, is the main efficiency bottleneck in FVFT-OBR. While advection-based remappers use the flux form to directly enforce mass conservation, the optimization setting allows us to treat mass conservation as one of the constraints. To take advantage of this fact, we consider an alternative mass-variable mass-target (MVMT-OBR) formulation in which the optimization variables are the net mass updates per cell and a single linear constraint enforces the conservation of mass. In so doing we change the structure of the OBR problem from a global linear-inequality constrained QP to a singly linearly constrained QP with simple bounds. Using the structure of the MVMT-OBR problem, and the fact that in remap the old and new grids are close, we are able to develop a simple, efficient and easily parallelizable optimization algorithm for the primal MVMT-OBR QP. Numerical studies on a variety of affine and non-affine grids confirm that MVMT-OBR is as accurate and robust as FVFT-OBR, but has the same computational cost as the explicit, state-of-the-art FCR.