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Volume 8, Issue 5
Trigonometric WENO Schemes for Hyperbolic Conservation Laws and Highly Oscillatory Problems

Jun Zhu & Jianxian Qiu

DOI: 10.4208/cicp.250509.211009a

Commun. Comput. Phys., 8 (2010), pp. 1242-1263.

Published online: 2010-08

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  • Abstract

In this paper, we use trigonometric polynomial reconstruction, instead of algebraic polynomial reconstruction, as building blocks for the weighted essentially non-oscillatory (WENO) finite difference schemes to solve hyperbolic conservation laws and highly oscillatory problems. The goal is to obtain robust and high order accurate solutions in smooth regions, and sharp and non-oscillatory shock transitions. Numerical results are provided to illustrate the behavior of the proposed schemes.

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@Article{CiCP-8-1242, author = {Jun Zhu and Jianxian Qiu}, title = {Trigonometric WENO Schemes for Hyperbolic Conservation Laws and Highly Oscillatory Problems}, journal = {Communications in Computational Physics}, year = {2010}, volume = {8}, number = {5}, pages = {1242--1263}, abstract = {

In this paper, we use trigonometric polynomial reconstruction, instead of algebraic polynomial reconstruction, as building blocks for the weighted essentially non-oscillatory (WENO) finite difference schemes to solve hyperbolic conservation laws and highly oscillatory problems. The goal is to obtain robust and high order accurate solutions in smooth regions, and sharp and non-oscillatory shock transitions. Numerical results are provided to illustrate the behavior of the proposed schemes.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.250509.211009a}, url = {http://global-sci.org/intro/article_detail/cicp/7615.html} }
TY - JOUR T1 - Trigonometric WENO Schemes for Hyperbolic Conservation Laws and Highly Oscillatory Problems AU - Jun Zhu & Jianxian Qiu JO - Communications in Computational Physics VL - 5 SP - 1242 EP - 1263 PY - 2010 DA - 2010/08 SN - 8 DO - http://doi.org/10.4208/cicp.250509.211009a UR - https://global-sci.org/intro/article_detail/cicp/7615.html KW - AB -

In this paper, we use trigonometric polynomial reconstruction, instead of algebraic polynomial reconstruction, as building blocks for the weighted essentially non-oscillatory (WENO) finite difference schemes to solve hyperbolic conservation laws and highly oscillatory problems. The goal is to obtain robust and high order accurate solutions in smooth regions, and sharp and non-oscillatory shock transitions. Numerical results are provided to illustrate the behavior of the proposed schemes.

Jun Zhu and Jianxian Qiu. (2010). Trigonometric WENO Schemes for Hyperbolic Conservation Laws and Highly Oscillatory Problems. Communications in Computational Physics. 8 (5). 1242-1263. doi:10.4208/cicp.250509.211009a
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