A Robust Reconstruction for Unstructured WENO Schemes

Authors:
Yuan Liu;Yong-Tao Zhang
Affiliations:
Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, USA 46556;Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, USA 46556
Venue:
Journal of Scientific Computing
Year:
2013

Citing 19
Cited 0

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Abstract

The weighted essentially non-oscillatory (WENO) schemes are a popular class of high order numerical methods for hyperbolic partial differential equations (PDEs). While WENO schemes on structured meshes are quite mature, the development of finite volume WENO schemes on unstructured meshes is more difficult. A major difficulty is how to design a robust WENO reconstruction procedure to deal with distorted local mesh geometries or degenerate cases when the mesh quality varies for complex domain geometry. In this paper, we combine two different WENO reconstruction approaches to achieve a robust unstructured finite volume WENO reconstruction on complex mesh geometries. Numerical examples including both scalar and system cases are given to demonstrate stability and accuracy of the scheme.