Improved detection criteria for the multi-dimensional optimal order detection (MOOD) on unstructured meshes with very high-order polynomials

Abstract

This paper extends the MOOD method proposed by the authors in [A high-order finite volume method for hyperbolic systems: Multi-dimensional Optimal Order Detection (MOOD)'', J. Comput. Phys. 230, pp 4028-4050, (2011)], 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 efectively high-order (up to sixth-order), intrinsincally positivity-preserving on hydrodynamics test cases and computationaly efficient.