TY - JOUR
T1 - A Multi-Domain Hybrid DG and WENO Method for Hyperbolic Conservation Laws on Hybrid Meshes
AU - Jian Cheng & Tiegang Liu
JO - Communications in Computational Physics
VL - 4
SP - 1116
EP - 1134
PY - 2014
DA - 2014/10
SN - 16
DO - http://doi.org/10.4208/cicp.060313.300514a
UR - https://global-sci.org/intro/article_detail/cicp/7075.html
KW - 
AB - <p style="text-align: justify;">In [SIAM J. Sci. Comput., 35(2)(2013), A1049–A1072], a class of multi-domain
hybrid DG and WENO methods for conservation laws was introduced. Recent applications of this method showed that numerical instability may encounter if the DG flux
with Lagrangian interpolation is applied as the interface flux during the moment of
conservative coupling. In this continuation paper, we present a more robust approach
in the construction of DG flux at the coupling interface by using WENO procedures of
reconstruction. Based on this approach, such numerical instability is overcome very
well. In addition, the procedure of coupling a DG method with a WENO-FD scheme
on 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 either
WENO-FD flux or DG flux at the moment of requiring conservative coupling.</p>