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

Published online by Cambridge University Press:  20 August 2015

Rui Zhang ,
Mengping Zhang  and
Chi-Wang Shu
Rui Zhang*
Affiliation:
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China
Mengping Zhang*
Affiliation:
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China
Chi-Wang Shu*
Affiliation:
Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
*
Email:rui@ustc.edu.cn
Email:mpzhang@ustc.edu.cn
Corresponding author.Email:shu@dam.brown.edu
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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.

Keywords

65M08Weighted essentially non-oscillatory (WENO) schemesfinite volume schemesaccuracy

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 9 , Issue 3 , March 2011 , pp. 807 - 827
Copyright
Copyright © Global Science Press Limited 2011

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