Commun. Comput. Phys., 9 (2011), pp. 807-827.


On the Order of Accuracy and Numerical Performance of Two Classes of Finite Volume WENO Schemes

Rui Zhang 1, Mengping Zhang 1, Chi-Wang Shu 2*

1 Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China.
2 Division of Applied Mathematics, Brown University, Providence, RI 02912, USA.

Received 29 November 2009; Accepted (in revised version) 8 April 2010
Available online 17 September 2010
doi:10.4208/cicp.291109.080410s

Abstract

In this paper we consider two commonly used classes of finite volume weighted essentially non-oscillatory (WENO) schemes in two dimensional Cartesian meshes. We compare them in terms of accuracy, performance for smooth and shocked solutions, and efficiency in CPU timing. For linear systems both schemes are high order accurate, however for nonlinear systems, analysis and numerical simulation results verify that one of them (Class A) is only second order accurate, while the other (Class B) is high order accurate. The WENO scheme in Class A is easier to implement and costs less than that in Class B. Numerical experiments indicate that the resolution for shocked problems is often comparable for schemes in both classes for the same building blocks and meshes, despite of the difference in their formal order of accuracy. The results in this paper may give some guidance in the application of high order finite volume schemes for simulating shocked flows.

AMS subject classifications: 65M08

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Key words: Weighted essentially non-oscillatory (WENO) schemes, finite volume schemes, accuracy.

*Corresponding author.
Email: rui@ustc.edu.cn (R. Zhang), mpzhang@ustc.edu.cn (M. Zhang), shu@dam.brown.edu (C.-W. Shu)
 

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