HIGH ORDER STABLE MULTI-DOMAIN HYBRID RKDG AND WENO-FD METHODS  

作　　者：Fan Zhang Tiegang Liu Jian Cheng 

机构地区：[1]School of Mathematics and Systems Science, Beihang University, Beijing 100191, China [2]Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

出　　处：《Journal of Computational Mathematics》2018年第4期517-541,共25页计算数学（英文）

基　　金：This work is partially supported under the National Natural Science Foundation of China No. 91530325, the Fundamental Research of Civil Aircraft MJ-F-2012-04, and National 973 project No.2012CB720205.

摘　　要：Recently, a kind of high order hybrid methods based on Runge-Kutta discontinu- ous 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.Recently, a kind of high order hybrid methods based on Runge-Kutta discontinu- ous 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.

关 键 词：Runge-Kutta discontinuous Galerkin method Weighted essentially non-oscillatory scheme Multi-domain hybrid method Conservation laws Heuristic theory 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构] O35[自动化与计算机技术—计算机科学与技术]