Commun. Comput. Phys., 5 (2009), pp. 836-848.


Third Order WENO Scheme on Three Dimensional Tetrahedral Meshes

Yong-Tao Zhang 1*, Chi-Wang Shu 2

1 Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556-4618, USA.
2 Division of Applied Mathematics, Brown University, Providence, RI 02912, USA.

Received 29 August 2007; Accepted (in revised version) 25 January 2008
Available online 1 August 2008

Abstract

We extend the weighted essentially non-oscillatory (WENO) schemes on two dimensional triangular meshes developed in \cite{HS} to three dimensions, and construct a third order finite volume WENO scheme on three dimensional tetrahedral meshes. We use the Lax-Friedrichs monotone flux as building blocks, third order reconstructions made from combinations of linear polynomials which are constructed on diversified small stencils of a tetrahedral mesh, and non-linear weights using smoothness indicators based on the derivatives of these linear polynomials. Numerical examples are given to demonstrate stability and accuracy of the scheme.

AMS subject classifications: 65M99

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

*Corresponding author.
Email: yzhang10@nd.edu (Y.-T. Zhang), shu@dam.brown.edu (C.-W. Shu)
 

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