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.
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