The Multidimensional Optimal Order Detection method in the three‐dimensional case: very high‐order finite volume method for hyperbolic systems
Tóm tắt
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.Copyright © 2013 John Wiley & Sons, Ltd.
Từ khóa
Tài liệu tham khảo
Kolgan VP, 1972, Application of the minimum‐derivative principle in the construction of finite‐difference schemes for numerical analysis of discontinuous solutions in gas dynamics, Transactions of the Central Aerohydrodynamics Institute, 3, 68
Kolgan VP, 1975, Finite‐difference schemes for computation of three dimensional solutions of gas dynamics and calculation of a flow over a body under an angle of attack, Transactions of the Central Aerohydrodynamics Institute, 6, 1
Zhang Y‐T, 2009, Third‐order WENO scheme on three dimensional tetrahedral meshes, Communications in Computational Physics, 5, 836