A New Fifth-Order Trigonometric WENO Scheme for Hyperbolic Conservation Laws and Highly Oscillatory Problems

A New Fifth-Order Trigonometric WENO Scheme for Hyperbolic Conservation Laws and Highly Oscillatory Problems

Year:    2019

Author:    Yanmeng Wang, Jun Zhu, Lianglin Xiong

Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 5 : pp. 1114–1135

Abstract

In this paper, we propose trigonometric polynomial reconstructions based on one five-point stencil and two two-point stencils, instead of algebraic polynomial reconstructions defined on three three-point stencils [20,35], as a building block for designing a fifth-order trigonometric weighted essentially non-oscillatory (TWENO) scheme to solve hyperbolic conservation laws and highly oscillatory problems. The main objective of the paper is to extremely reduce the difficulty in computing the linear weights, could get less absolute truncation errors in smooth regions, and keep sharp shock transitions in nonsmooth regions. Extensive benchmark numerical tests including some highly oscillatory problems are provided to verify the good performance of the new scheme.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2018-0221

Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 5 : pp. 1114–1135

Published online:    2019-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    22

Keywords:    Trigonometric polynomial reconstruction hyperbolic conservation laws highly oscillatory problem WENO scheme.

Author Details

Yanmeng Wang

Jun Zhu

Lianglin Xiong

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