An alternative finite difference weno-like scheme with physical constraint preservation for divergence-preserving hyperbolic systems

Abstract

Alternative finite difference Weighted Essentially Non-Oscillatory (AFD-WENO) schemes allow us to very efficiently update hyperbolic systems even in complex geometries. Recent innovations in AFD-WENO methods allow us to treat hyperbolic system with non-conservative products almost as efficiently as conservation laws. However, some PDE systems,like computational electrodynamics (CED) and magnetohydrodynamics (MHD) and relativistic magnetohydrodynamics (RMHD), have involution constraints that require divergence-free or divergence-preserving evolution of vector fields. In such situations, a Yee-style collocation of variables proves indispensable; and that collocation is retained in this work. In previous works, only higher order finite volume discretization of such involution constrained systems was possible. In this work, we show that substantially more efficient AFD-WENO methods have been extended to encompass divergence-preserving hyperbolic PDEs.