Hermite WENO Schemes with Strong Stability Preserving Multi-Step Temporal Discretization Methods for Conservation Laws

Hermite WENO Schemes with Strong Stability Preserving Multi-Step Temporal Discretization Methods for Conservation Laws

Year:    2017

Author:    Xiaofeng Cai, Jun Zhu, Jianxian Qiu

Journal of Computational Mathematics, Vol. 35 (2017), Iss. 1 : pp. 52–73

Abstract

Based on the work of Shu [SIAM J. Sci. Stat. Comput, 9 (1988), pp.1073-1084], we construct a class of high order multi-step temporal discretization procedure for finite volume Hermite weighted essential non-oscillatory (HWENO) methods to solve hyperbolic conservation laws. The key feature of the multi-step temporal discretization procedure is to use variable time step with strong stability preserving (SSP). The multi-step temporal discretization methods can make full use of computed information with HWENO spatial discretization by holding the former computational values. Extensive numerical experiments are presented to demonstrate that the finite volume HWENO schemes with multi-step discretization can achieve high order accuracy and maintain non-oscillatory properties near discontinuous region of the solution.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1609-m2014-0069

Journal of Computational Mathematics, Vol. 35 (2017), Iss. 1 : pp. 52–73

Published online:    2017-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    22

Keywords:    Multi-step temporal discretization Hermite weighted essentially non-oscillatory scheme Uniformly high order accuracy Strong stability preserving Finite volume scheme.

Author Details

Xiaofeng Cai

Jun Zhu

Jianxian Qiu

  1. Positivity-preserving high order finite volume hybrid Hermite WENO schemes for compressible Navier-Stokes equations

    Fan, Chuan | Zhang, Xiangxiong | Qiu, Jianxian

    Journal of Computational Physics, Vol. 445 (2021), Iss. P.110596

    https://doi.org/10.1016/j.jcp.2021.110596 [Citations: 15]
  2. Finite-Difference Hermite WENO Scheme for Degasperis-Procesi Equation

    Li, Liang | Feng, Yapu | Wang, Yanmeng | Pang, Liuyong | Zhu, Jun

    Processes, Vol. 11 (2023), Iss. 5 P.1536

    https://doi.org/10.3390/pr11051536 [Citations: 0]
  3. Fifth-Order Hermite Targeted Essentially Non-oscillatory Schemes for Hyperbolic Conservation Laws

    Wibisono, Indra | Kosasih, Engkos A.

    Journal of Scientific Computing, Vol. 87 (2021), Iss. 3

    https://doi.org/10.1007/s10915-021-01485-0 [Citations: 16]
  4. A Modified Fifth Order Finite Difference Hermite WENO Scheme for Hyperbolic Conservation Laws

    Zhao, Zhuang | Zhang, Yong-Tao | Qiu, Jianxian

    Journal of Scientific Computing, Vol. 85 (2020), Iss. 2

    https://doi.org/10.1007/s10915-020-01347-1 [Citations: 13]