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Improved detection criteria for the multi-dimensional optimal order detection (MOOD) on unstructured meshes with very high-order polynomials. (English) Zbl 1365.76149
Summary: This paper extends the MOOD method proposed by the authors in [J. Comput. Phys. 230, No. 10, 4028–4050 (2011; Zbl 1218.65091)], along two complementary axes: extension to very high-order polynomial reconstruction on non-conformal unstructured meshes and new detection criteria. The former is a natural extension of the previous cited work which confirms the good behavior of the MOOD method. The latter is a necessary brick to overcome limitations of the discrete maximum principle used in the previous work. Numerical results on advection problems and hydrodynamics Euler equations are presented to show that the MOOD method is effectively high-order (up to sixth-order), intrinsically positivity-preserving on hydrodynamics test cases and computationally efficient.

76M12 Finite volume methods applied to problems in fluid mechanics
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
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