CESAR

Scalably efficient, high-order accurate ($ p \ge 2 $) multimesh interpolators that are conservative (in the global sense), and minimally dissipative (locally) to compute solution variations on unstructured meshes are critically important for several multiphysics problems to obtain consistent field transfers. Whether the interpolator is based on traditional nearest neighbor interpolants ($ \mathcal{O}(1) $) or more advanced, high-order ($ \mathcal{O} (\ge 2) $) conservative and monotone, linear and nonlinear maps for field projections, the accuracy, computational cost and behavior of the resulting coupled system will be significantly different. Understanding the right algorithm to find the balance in efficiency and accuracy (efficacy) is hence often necessary for many simulations in nuclear engineering and climatology.

Since the computation of the intersection between source and target component meshes is a crucial step in generating conservative linear maps during multimesh transfers, significant effort has been invested in creating scalable, topological mesh intersection algorithms for climate science applications already. However, extensions to arbitrary dimensional unstructured meshes remain a topic of open research. Another interesting research path is to reformulate the global coupled nonlinear problem as a spacetime remap constrained optimization, which can guarantee the right conservative fluxes at component domain interfaces (surface coupling), and scalar high-order interpolants for homogeneous subdomains (volumetric coupling). This approach exposes an integral treatment of all nonlinear spatiotemporal approximations in a unified formulation and could yield better accuracy and stability in the resultant solver.