The Multidimensional Optimal Order Detection method in the three‐dimensional case: very high‐order finite volume method for hyperbolic systems

International Journal for Numerical Methods in Fluids - Tập 73 Số 4 - Trang 362-392 - 2013
Steven Diot1, Raphaël Loubère1, Stéphane Clain1,2
1Institut de Mathématiques de Toulouse, CNRS Université de Toulouse 31062 Toulouse France
2Mathematical Centre, Minho University, 4710-057 Braga, Portugal

Tóm tắt

SUMMARYThe 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.

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Thông tin xuất bản

International Journal for Numerical Methods in Fluids

Tập 73 Số 4

362-392

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