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WENO schemes for mixed-element unstructured meshes. (English) Zbl 1364.76121
Summary: The paper extends weighted essentially non-oscillatory (WENO) schemes to two-dimensional quadrilateral and mixed-element unstructured meshes. The key element of the proposed methods is a reconstruction procedure suitable for arbitrarily-shaped cells. The resulting schemes achieve the designed uniformly high-order of accuracy and compute discontinuous solutions without spurious oscillations at interfaces between cells of two different types.

MSC:
76M12 Finite volume methods applied to problems in fluid mechanics
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
76M10 Finite element methods applied to problems in fluid mechanics
Software:
HLLE
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