The Multidimensional Optimal Order Detection method in the three‐dimensional case: very high‐order finite volume method for hyperbolic systems
The Multidimensional Optimal Order Detection method in the three‐dimensional case: very high‐order finite volume method for hyperbolic systems
复制标题
三维情况下的多维最优阶检测方法：双曲系统的甚高阶有限体积法
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
S. Clain
中科院分区：
文献类型：
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作者：
S. Diot;R. Loubère;S. Clain
作者在最近的两篇论文中介绍了二维几何的多维最优阶检测（MOOD）方法。在这里，我们提出了扩展到三维混合网格组成的四面体，六面体，金字塔，和棱柱。此外，我们简化了以前开发的U2检测过程，并在对流方程和欧拉系统的相关数值试验中显示，光滑解达到最佳高阶精度，而防止了奇点附近的虚假振荡。最后，在三维空间中验证了MOOD方法的保正性，并给出了一些简单的优化方法来降低计算量，使得MOOD方法与现有的高阶有限体积方法相比具有很强的竞争力。Copyright © 2013 John Wiley & Sons，Ltd.
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.
影响因子：
4.1
作者：
Dumbser, Michael;Balsara, Dinshaw S.;Munz, Claus-Dieter
通讯作者：
Munz, Claus-Dieter