The multidimensional optimal order detection method in the three-dimensional case : very high-order finite volume method for hyperbolic systems

Abstract

The Multidimensional Optimal Order Detection (MOOD) method for two-dimensional geometries has been introduced by the authors in two recent papers.We present here the extension to 3D mixed meshes composed of tetrahedra, hexahedra, pyramids, and prisms. In addition, we simplify the u2 detection process previously developed and show on a relevant set of numerical tests for both the convection equation and the Euler system that the optimal high order of accuracy is reached on smooth solutions, whereas spurious oscillations near singularities are prevented. At last, the intrinsic positivity-preserving property of the MOOD method is confirmed in 3D, and we provide simple optimizations to reduce the computational cost such that the MOOD method is very competitive compared with existing high-order Finite Volume methods.