A New Fifth-Order Finite Volume Central WENO Scheme for Hyperbolic Conservation Laws on Staggered Meshes

A New Fifth-Order Finite Volume Central WENO Scheme for Hyperbolic Conservation Laws on Staggered Meshes

Year:    2022

Author:    Shengzhu Cui, Zhanjing Tao, Jun Zhu

Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 5 : pp. 1059–1086

Abstract

In this paper, a new fifth-order finite volume central weighted essentially non-oscillatory (CWENO) scheme is proposed for solving hyperbolic conservation laws on staggered meshes. The high-order spatial reconstruction procedure using a convex combination of a fourth degree polynomial with two linear polynomials (in one dimension) or four linear polynomials (in two dimensions) in a traditional WENO fashion and a time discretization method using the natural continuous extension (NCE) of the Runge-Kutta method are applied to design this new fifth-order CWENO scheme. This new finite volume CWENO scheme uses the information defined on the same largest spatial stencil as that of the same order classical CWENO schemes [37, 46] with the application of smaller number of unequal-sized spatial stencils. Since the new nonlinear weights are adopted, the new finite volume CWENO scheme could obtain the same order of accuracy and get smaller truncation errors in $L^1$ and $L^∞$ norms in smooth regions, and control the spurious oscillations near strong shocks or contact discontinuities. The new CWENO scheme has advantages over the classical CWENO schemes [37, 46] on staggered meshes in its simplicity and easy extension to multi-dimensions. Some one-dimensional and two-dimensional benchmark numerical examples are provided to illustrate the good performance of this new fifth-order finite volume CWENO scheme.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2021-0095

Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 5 : pp. 1059–1086

Published online:    2022-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    28

Keywords:    Finite volume scheme central WENO scheme NCE of Runge-Kutta method staggered mesh.

Author Details

Shengzhu Cui

Zhanjing Tao

Jun Zhu

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    https://doi.org/10.1016/j.jcp.2024.112927 [Citations: 0]