基于非结构/混合网格模拟黏性流的高阶精度DDG/FV混合方法

邵帅; 李明; 王年华; 张来平

doi:10.6052/0459-1879-18-199

基于非结构/混合网格模拟黏性流的高阶精度DDG/FV混合方法

邵帅^*,2),,
李明^*,
王年华^*,
张来平^*†3), ,

^*中国空气动力研究与发展中心计算空气动力研究所, 四川绵阳 621000
^†中国空气动力研究与发展中心空气动力学国家重点实验室, 四川绵阳 621000

基金项目: 1) 国家重点研发计划(2016YFB0200700) 和自然科学基金重大研究计划集成项目(91530325) 资助.

详细信息

作者简介:
null

2) 邵帅, 硕士, 主要研究方向: 非结构网格高精度数值算法. E-mail: shaoshuai951413@gmail.com

通讯作者:
张来平

中图分类号: V211.3;
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出版历程
- 刊出日期: 2018-11-17

HIGH-ORDER DDG/FV HYBRID METHOD FOR VISCOUS FLOW SIMULATION ON UNSTRUCTURED/HYBRID GRIDS

Shao Shuai^*,2),,
Li Ming^*,
Wang Nianhua^*,
Zhang Laiping^*†3), ,

^*Computational Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang 621000, Sichuan, China
^†State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang 621000, Sichuan, China

摘要

摘要: 间断Galerkin有限元方法(discontinuous Galerkin method, DGM) 因具有计算精度高、模板紧致、易于并行等优点, 近年来已成为非结构/混合网格上广泛研究的高阶精度数值方法. 但其计算量和内存需求量巨大, 特别是对于网格规模达到百万甚至数千万的大型三维实际复杂外形问题, 其计算量和存储量对计算资源的消耗是难以承受的. 基于“混合重构”的DG/FV 格式可以有效降低DGM 的计算量和存储量. 本文将DDG 黏性项离散方法推广应用于DG/FV 混合算法, 得到新的DDG/FV混合格式, 以进一步提高DG/FV混合算法对于黏性流动模拟的计算效率. 通过Couette流动、层流平板边界层、定常圆柱绕流, 非定常圆柱绕流和NACA0012 翼型绕流等二维黏性流算例, 优化了DDG 通量公式中的参数选择, 验证了DDG/FV 混合格式对定常和非定常黏性流模拟的精度和计算效率, 并与广泛使用的BR2-DG 格式的计算结果和效率进行对比研究. 一系列数值实验结果表明, 本文构造的DDG/FV混合格式在二维非结构/混合网格的Navier-Stokes 方程求解中, 在达到相同的数值精度阶的前提下, 相比BR2-DG格式, 对于隐式时间离散的定常问题计算效率提高了2 倍以上, 对于显式时间离散的非定常问题计算效率提高1.6 倍, 并且在一些算例中, 混合格式具有更优良的计算稳定性. DDG/FV 混合格式提升了计算效率和稳定性, 具有良好的应用前景.
- 直接间断迦辽金方法DDG /
- DG/FV混合算法 /
- 高阶精度数值方法 /
- 非结构/混合网格
Abstract: In recent years, the discontinuous Galerkin method (DGM) has become one of the most popular high-order methods on unstructured/hybrid grids due to its excellent features: high accuracy, compact stencils and high parallelizability. At the same time, DGM is recognized as computationally intensive with respect to both computational costs and storage requirements. When it simulates the flow over 3D realistic complex configuration with large-scale grid, the huge memory requirements and high computational costs of DG method are usually unbearable. Recently, based on the idea of `hybrid reconstruction', a class of DG/FV hybrid schemes has been proposed and developed, which can successfully reduce the expensive computational costs and memory requirements. In this work, we introduce the efficient viscous term discretization method DDG into DG/FV method, and get a new hybrid scheme named as DDG/FV in order to further improve the efficiency of DG/FV scheme for simulating viscous flow problems. A variety of typical 2D laminar cases are tested, including Couette flow, laminar flow over a flat plate, steady flow over a cylinder, unsteady flow over a cylinder, and laminar flow over a NACA0012 airfoil. According to these cases, we select proper coefficients for DDG formulation, verify the order of accuracy and computational efficiency of DDG/FV for the simulation of steady and unsteady viscous flow, and compare the simulation results and computational efficiency with the widely used BR2-DG scheme. The numerical results demonstrate that the new DDG/FV hybrid scheme can achieve the designed order of accuracy. It can achieve the same accuracy as BR2-DG scheme with efficiency increased by more than 2 times for steady problems with implicit time scheme and by 1.6 times for unsteady problems with explicit time scheme in solving Navier-Stokes equations on unstructured/hybrid grids. And in some cases, the DDG/FV scheme has stronger robustness than the BR2-DG scheme. Because of the improvement of efficiency and robustness, the DDG/FV hybrid scheme shows good potential in future applications.
- direct discontinuous Galerkin method /
- DG/FV hybrid method /
- high order method /
- unstructured/hybrid grids

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参考文献(1)

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