High Order Stable Multi-Domain Hybrid RKDG and WENO-FD Methods

High Order Stable Multi-Domain Hybrid RKDG and WENO-FD Methods

Year:    2018

Author:    Fan Zhang, Jian Cheng, Tiegang Liu

Journal of Computational Mathematics, Vol. 36 (2018), Iss. 4 : pp. 517–541

Abstract

Recently, a kind of high order hybrid methods based on Runge-Kutta discontinuous Galerkin (RKDG) method and weighted essentially non-oscillatory finite difference (WENO-FD) scheme was proposed. Those methods are computationally efficient, however, stable problems might sometimes be encountered in practical applications. In this work, we first analyze the linear stabilities of those methods based on the Heuristic theory. We find that the conservative hybrid method is linearly unstable if the numerical flux at the coupling interface is chosen to be 'downstream'. Then we introduce two ways of healing this defect. One is to choose the numerical flux at the coupling interface to be 'upstream'. The other is to employ a slope limiter function to enforce the hybrid method satisfying the local total variation diminishing (TVD) condition. In the end, numerical experiments are provided to validate the effectiveness of the proposed methods.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1702-m2016-0707

Journal of Computational Mathematics, Vol. 36 (2018), Iss. 4 : pp. 517–541

Published online:    2018-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    25

Keywords:    Runge-Kutta discontinuous Galerkin method Weighted essentially non-oscillatory scheme Multi-domain hybrid method Conservation laws Heuristic theory.

Author Details

Fan Zhang

Jian Cheng

Tiegang Liu