Methods and Applications of Analysis

Volume 21 (2014)

Number 1

Free-stream preserving finite difference schemes on curvilinear meshes

Pages: 1 – 30

DOI: http://dx.doi.org/10.4310/MAA.2014.v21.n1.a1

Authors

Yan Jiang (School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui, China)

Chi-Wang Shu (Division of Applied Mathematics, Brown University, Providence, Rhode Island, U.S.A.)

Mengping Zhang (School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui, China)

Abstract

An important property for finite difference schemes designed on curvilinear meshes is the exact preservation of free-stream solutions. This property is difficult to fulfill for high order conservative essentially non-oscillatory (WENO) finite difference schemes. In this paper we explore an alternative flux formulation for such finite difference schemes [5] which can preserve free-stream solutions, based on the numerical technique for the metric terms [13], which can be applied to this alternative flux formulation but is difficult to be applied to the standard finite difference formulation. Free-stream and vortex preservation properties are investigated, and comparison with standard finite difference WENO schemes is made. Theoretical derivation and numerical results show that the finite difference WENO schemes based on the alternative flux formulation can preserve free-stream and vortex solutions on both stationary and dynamically generalized coordinate systems, hence giving much better performance than the standard finite difference WENO schemes for such problems.

Keywords

high order finite difference scheme, weighted essentially non-oscillatory scheme, curvilinear meshes

2010 Mathematics Subject Classification

65M06

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