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Volume 16, Issue 4
A Multi-Domain Hybrid DG and WENO Method for Hyperbolic Conservation Laws on Hybrid Meshes

Jian Cheng & Tiegang Liu

DOI: 10.4208/cicp.060313.300514a

Commun. Comput. Phys., 16 (2014), pp. 1116-1134.

Published online: 2014-10

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  • Abstract

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.

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@Article{CiCP-16-1116, author = {Jian Cheng and Tiegang Liu}, title = {A Multi-Domain Hybrid DG and WENO Method for Hyperbolic Conservation Laws on Hybrid Meshes}, journal = {Communications in Computational Physics}, year = {2014}, volume = {16}, number = {4}, pages = {1116--1134}, abstract = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.060313.300514a}, url = {http://global-sci.org/intro/article_detail/cicp/7075.html} }
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 -

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.

Jian Cheng and Tiegang Liu. (2014). A Multi-Domain Hybrid DG and WENO Method for Hyperbolic Conservation Laws on Hybrid Meshes. Communications in Computational Physics. 16 (4). 1116-1134. doi:10.4208/cicp.060313.300514a
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