A Multi-Domain Hybrid DG and WENO Method for Hyperbolic Conservation Laws on Hybrid Meshes (Communications in Computational Physics, 2014)
In [SIAM J. Sci. Comput., 35(2)(2013), A1049–A1072], a class of multi-domainhybrid DG and WENO methods for conservation laws was introduced. Recent applications of this method showed that numerical instability may encounter if the DG fluxwith Lagrangian interpolation is applied as the interface flux during the moment ofconservative coupling. In this continuation paper, we present a more robust approachin the construction of DG flux at the coupling interface by using WENO procedures ofreconstruction. Based on this approach, such numerical instability is overcome verywell. In addition, the procedure of coupling a DG method with a WENO-FD schemeon hybrid meshes is disclosed in detail. Typical testing cases are employed to demonstrate the accuracy of this approach and the stability under the flexibility of using eitherWENO-FD flux or DG flux at the moment of requiring conservative coupling.