基于非结构/混合网格的高阶精度格式研究进展

张来平; 贺立新; 刘伟; 李明; 张涵信

doi:10.6052/1000-0992-12-092

基于非结构/混合网格的高阶精度格式研究进展

doi: 10.6052/1000-0992-12-092

张来平^1,2, ,,
贺立新²,
刘伟^1,2,
李明²,
张涵信²

1 空气动力学国家重点实验室, 四川绵阳 621000
2 中国空气动力研究与发展中心, 四川绵阳 621000

基金项目: 国家重点基础研究发展计划(973) (2009CB723802)和国家自然科学基金(91016001, 91016011, 91130029)资助项目

详细信息

作者简介:
张来平, 1968 年出生, 1990 年毕业于中国科学技术大学近代力学系, 1997 年中国空气动力研究与发展中心博士. 现任中国空气动力研究与发展中心计算空气动力研究所研究员, 空气动力学学会理事, 中国力学学会青年工作委员会委员. 主要从事非结构/混合网格生成技术、基于非结构/混合网格的计算格式、非定常流动机理等方面的研究与应用工作.

通讯作者:
张来平

中图分类号: V211.3
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出版历程
- 收稿日期: 2012-08-28
- 修回日期: 2013-03-19
- 刊出日期: 2013-03-25

Reviews of high-order methods on unstructured and hybrid grid

ZHANG Laiping^{1,2
, ,},
HE Lixin²,
LIU Wei^1,2,
LI Ming²,
ZHANG Hanxin²

1 State Key Laboratory of Aerodynamics, Sichuan, Mianyang 621000, China
2 China Aerodynamics Research and Development Center, Sichuan, Mianyang 621000, China

Funds: The project was supported by the National Basic Research Program of China (973 Program) (2009CB723802), the Natural Science Foundation of China (91016001, 91016011, 91130029).

More Information

Corresponding author: ZHANG Laiping

摘要

摘要: 尽管以二阶精度格式为基础的计算流体力学(CFD) 方法和软件已经在航空航天飞行器设计中发挥了重要的作用, 但是由于二阶精度格式的耗散和色散较大, 对于湍流、分离等多尺度流动现象的模拟, 现有成熟的CFD 软件仍难以给出满意的结果, 为此CFD 工作者发展了众多的高阶精度计算格式. 如果以适应的计算网格来分类, 一般可以分为基于结构网格的有限差分格式、基于非结构/混合网格的有限体积法和有限元方法,以及各种类型的混合方法. 由于非结构/混合网格具有良好的几何适应性, 基于非结构/混合网格的高阶精度格式近年来备受关注. 本文综述了近年来基于非结构/混合网格的高阶精度格式研究进展, 重点介绍了空间离散方法, 主要包括k-Exact 和ENO/WENO 等有限体积方法, 间断伽辽金(DG) 有限元方法, 有限谱体积(SV) 和有限谱差分(SD) 方法, 以及近来发展的各种DG/FV 混合算法和将各种方法统一在一个框架内的CPR (correctionprocedure via reconstruction) 方法等. 随后简要介绍了高阶精度格式应用于复杂外形流动数值模拟的一些需要关注的问题, 包括曲边界的处理方法、间断侦测和限制器、各种加速收敛技术等. 在综述过程中, 介绍了各种方法的优势与不足, 其间介绍了作者发展的基于"静动态混合重构" 的DG/FV 混合算法. 最后展望了基于非结构/混合网格的高阶精度格式的未来发展趋势及应用前景.
- 非结构网格 /
- 混合网格 /
- 高阶精度格式 /
- 有限体积方法 /
- 间断伽辽金方法 /
- 有限谱体积方法 /
- 有限谱差分方法 /
- DG/FV 混合算法
Abstract: While 2nd order methods are dominant in most compressible flow simulations, many types of problems, such as computational aeroacoustics (CAA), vortex-dominant flows and large eddy simulation (LES) of turbulent flows, call for higher order accuracy (third order and more). The main deficiency of widely available, second-order methods for the accurate simulations of the above-mentioned flows is the numerical diffusion and dissipation of vorticity to unacceptable level. Applications of high-order accu- rate, low-diffusion and low dissipation numerical methods can significantly alleviate this deficiency of the traditional second order methods, improve predictions of vortical and other complex, separated, unsteady flows. On the other hand, for complex configurations, the structured/unstructured hybrid grid technique presents the trend of grid generation technique. Therefore the high-order methods on unstructured and hybrid (or mixed) grids are paid much more attention in recent years. In this paper, the high-order methods on unstructured and hybrid grids are reviewed comprehensively, including the k-exact finite volume (FV) methods, the FV methods based on ENO and WENO reconstruction, the discontinuous Galerkin (DG) finite element method, the finite spectral volume (SV) methods, the finite spectral dif- ference (SD) method, DG/FV hybrid methods, the unified method based on correction procedure via reconstruction (CPR). The main ideas of these high-order methods are introduced, and the advantages and disadvantages of these methods are discussed. In addition, some important issues for simulations of complex geometry are discussed, including the treatment of curved boundary, the detector of discontinu-ity and high-order limiters, implicit iteration methods, and hp-multigrid approaches. We believe that the high-order methods on unstructured and hybrid grids will play more and more important role on more accurate simulations of realistic airspace vehicles and study of complex flow mechanism in the future.
- unstructured grid /
- hybrid grid /
- high-order method /
- finite element method /
- discontinuous Galerkin method /
- finite spectral volume method /
- finite spectral difference method /
- hybrid DG/FV methods

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