Efficient WENO-Based Prolongation Strategies for Divergence-Preserving Vector Fields

Abstract Adaptive mesh refinement (AMR) is the art of solving PDEs on a hierarchy with increasing at each level hierarchy. Accurate treatment AMR hierarchies requires accurate prolongation solution from coarse to newly defined finer mesh. For scalar variables, suitably high-order finite volume WENO methods can carry out such prolongation. However, classes PDEs, as computational electrodynamics (CED) and magnetohydrodynamics (MHD), require that vector fields preserve divergence constraint. The primal variables in schemes consist normal components field are collocated faces As result, reconstruction strategies for constraint-preserving necessarily more intricate. In this paper we present fourth-order strategy analytically exact. Extension higher orders using exact very challenging. To overcome challenge, novel WENO-like invented matches moments faces, where collocated. This approach almost constraint-preserving, therefore, call it WENO-ADP. make exactly touch-up procedure developed based constrained least squares (CLSQ) method restoring constraint up machine accuracy. With touch-up, called WENO-ADPT. It shown ratios two be accommodated. An item broader interest work have also been able invent efficient methods, coefficients easily obtained multidimensional smoothness indicators expressed perfect squares. We demonstrate works several high divergence-free well fields, has match charge density its moments. show our late time instability known plague adaptive computations CED.