A General High-Order Multi-Domain Hybrid DG/WENO-FD Method for Hyperbolic Conservation Laws

Abstract

In this paper, a general high-order multi-domain hybrid DG/WENO-FD method, which couples a $p^{th}$-order ($p$ ≥ 3) DG method and a $q^{th}$-order ($q$ ≥ 3) WENO-FD scheme, is developed. There are two possible coupling approaches at the domain interface, one is non-conservative, the other is conservative. The non-conservative coupling approach can preserve optimal order of accuracy and the local conservative error is proved to be upmost third order. As for the conservative coupling approach, accuracy analysis shows the forced conservation strategy at the coupling interface deteriorates the accuracy locally to first-order accuracy at the 'coupling cell'. A numerical experiments of numerical stability is also presented for the non-conservative and conservative coupling approaches. Several numerical results are presented to verify the theoretical analysis results and demonstrate the performance of the hybrid DG/WENO-FD solver.