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Volume 5, Issue 2-4
Third Order WENO Scheme on Three Dimensional Tetrahedral Meshes

Yong-Tao Zhang & Chi-Wang Shu

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

Published online: 2009-02

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  • Abstract

We extend the weighted essentially non-oscillatory (WENO) schemes on two dimensional triangular meshes developed in [7] 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.

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COPYRIGHT: © Global Science Press

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@Article{CiCP-5-836, author = {Yong-Tao Zhang and Chi-Wang Shu}, title = {Third Order WENO Scheme on Three Dimensional Tetrahedral Meshes}, journal = {Communications in Computational Physics}, year = {2009}, volume = {5}, number = {2-4}, pages = {836--848}, abstract = {

We extend the weighted essentially non-oscillatory (WENO) schemes on two dimensional triangular meshes developed in [7] 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.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7766.html} }
TY - JOUR T1 - Third Order WENO Scheme on Three Dimensional Tetrahedral Meshes AU - Yong-Tao Zhang & Chi-Wang Shu JO - Communications in Computational Physics VL - 2-4 SP - 836 EP - 848 PY - 2009 DA - 2009/02 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7766.html KW - AB -

We extend the weighted essentially non-oscillatory (WENO) schemes on two dimensional triangular meshes developed in [7] 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.

Yong-Tao Zhang and Chi-Wang Shu. (2009). Third Order WENO Scheme on Three Dimensional Tetrahedral Meshes. Communications in Computational Physics. 5 (2-4). 836-848. doi:
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