Arbitrary high-order non-oscillatory scheme on hybrid unstructured grids based on multi-moment finite volume method
Arbitrary high-order non-oscillatory scheme on hybrid unstructured grids based on multi-moment finite volume method
复制标题
基于多矩有限体积法的混合非结构网格任意高阶非振荡格式
DOI：
10.1016/j.jcp.2020.109841
复制
发表时间：
2021
影响因子：
4.1
通讯作者：
Xiao Feng
中科院分区：
文献类型：
--
作者：
Xie Bin;Deng Xi;Liao ShiJun;Xiao Feng
在这篇文章中，我们提出了一种新的高阶多矩有限体积方法（MMFVM），用于在非结构网格上求解线性和非线性双曲型方程组。与以往的体积平均/点值多矩（VPM）格式不同，本文提出了一种基于约束最小二乘法的新的重建方法，该方法可以自然地扩展到二维和三维任意高阶精度。所谓的VPM-CLS（基于约束最小二乘方法的VPM）方案大大提高了紧凑模板上的解的精度，大大简化了计算。为了消除高阶格式带来的数值振荡，提出了一种新的有限投影方法AOD（adaptive order detection），用于在存在间断解的情况下选择最优的重构多项式阶数.由此产生的重建方法，即VPM-AOD相结合的VPM-CLS计划与AOD限制投影技术是能够达到5阶精度的所有直接相邻的细胞的模板上，并实现基本上无振荡和较少的耗散的数值结果的不连续的解决方案。可压缩气体动力学欧拉方程的各种基准测试的数值方法进行了广泛的验证。数值结果表明，高的解决方案的精度和优秀的能力，提出的计划，以处理复杂的物理和几何。
In this article, we propose a novel high-order multi-moment finite volume method (MMFVM) for solving linear and nonlinear hyperbolic systems on unstructured grids. Different from the previous versions of volume-average/point-value multi-moment (VPM) scheme, the present scheme is developed by using a new reconstruction procedure based on the constrained least-square method which can be naturally extended to arbitrary high-order of accuracy in two and three dimensions. The so-called VPM-CLS (VPM based on constrained least-square method) scheme substantially increases the solution accuracy on a compact stencil which largely simplifies the computations. In order to eliminate the numerical oscillations associated with high-order schemes, we propose a new limiting projection approach named AOD (adaptive order detection) to choose the optimal degree of reconstruction polynomial for trouble cells in presence of discontinuous solutions. The resulting reconstruction method, i.e. VPM-AOD that combines VPM-CLS scheme with AOD limiting projection technique is able to attain 5th-order accuracy on the stencil of all immediately adjacent cells and achieve essentially non-oscillatory and less-dissipative numerical results for discontinuous solutions. The numerical methods are extensively verified by various benchmark tests for the Euler equations of compressible gas dynamics. Numerical results demonstrate the high solution accuracy and excellent capabilities of proposed schemes to handle both complex physics and geometries.
登录
查看更多内容
在非结构化网格上使用新型 WENO 限制器的 Runge-Kutta 不连续 Galerkin 方法
影响因子：
4.1
作者：
Zhu, Jun;Zhong, Xinghui;Shu, Chi-Wang;Qiu, Jianxian
通讯作者：
Qiu, Jianxian
影响因子：
2.5
作者：
A. Rault;G. Chiavassa;R. Donat
通讯作者：
A. Rault;G. Chiavassa;R. Donat
影响因子：
2.5
作者：
Z. Wang;Yen Liu;G. May;A. Jameson
通讯作者：
Z. Wang;Yen Liu;G. May;A. Jameson
DOI：
10.2514/6.2011-382
发表时间：
2011-01
期刊：
--
影响因子：
--
作者：
Timothy A. Eymann;P. Roe
通讯作者：
Timothy A. Eymann;P. Roe
DOI：
10.2514/6.1999-3259
发表时间：
1999-11
期刊：
--
影响因子：
--
作者：
M. Delanaye;Yen Liu
通讯作者：
M. Delanaye;Yen Liu