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


Trigonometric WENO Schemes for Hyperbolic Conservation Laws and Highly Oscillatory Problems

Jun Zhu 1, Jianxian Qiu 2*

1 College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 210016, China.
2 Department of Mathematics, Nanjing University, Nanjing, Jiangsu 210093, China.

Received 25 May 2009; Accepted (in revised version) 21 October 2009
Available online 28 July 2010
doi:10.4208/cicp.250509.211009a

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.

AMS subject classifications: 65M06, 65M99, 35L65

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Key words: TWENO scheme, hyperbolic conservation laws, highly oscillatory problem, finite difference scheme.

*Corresponding author.
Email: zhujun@nuaa.edu.cn (J. Zhu), jxqiu@nju.edu.cn (J. Qiu)
 

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