Volume 11, Issue 5
A New Fifth-Order Trigonometric WENO Scheme for Hyperbolic Conservation Laws and Highly Oscillatory Problems

Yanmeng Wang, Jun Zhu & Lianglin Xiong

Adv. Appl. Math. Mech., 11 (2019), pp. 1114-1135.

Published online: 2019-06

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  • 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.


  • Keywords

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

  • AMS Subject Headings

65M60, 35L65

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-11-1114, author = {}, title = {A New Fifth-Order Trigonometric WENO Scheme for Hyperbolic Conservation Laws and Highly Oscillatory Problems}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2019}, volume = {11}, number = {5}, pages = {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.


}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2018-0221}, url = {http://global-sci.org/intro/article_detail/aamm/13203.html} }
TY - JOUR T1 - A New Fifth-Order Trigonometric WENO Scheme for Hyperbolic Conservation Laws and Highly Oscillatory Problems JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 1114 EP - 1135 PY - 2019 DA - 2019/06 SN - 11 DO - http://dor.org/10.4208/aamm.OA-2018-0221 UR - https://global-sci.org/intro/aamm/13203.html KW - Trigonometric polynomial reconstruction, hyperbolic conservation laws, highly oscillatory problem, WENO scheme. AB -

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.


Yanmeng Wang, Jun Zhu & Lianglin Xiong. (2019). A New Fifth-Order Trigonometric WENO Scheme for Hyperbolic Conservation Laws and Highly Oscillatory Problems. Advances in Applied Mathematics and Mechanics. 11 (5). 1114-1135. doi:10.4208/aamm.OA-2018-0221
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