基于间断Galerkin有限元方法的高精度流场数值模拟研究
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- 英文论文题名：High-Order Discontinuous Galerkin Solution of three-dimensional simulations
- 论文作者：秦望龙 ; 吕宏强 ; 陈正武
- 年：2016
- 作者机构：南京航空航天大学航空宇航学院;中国空气动力学研究与发展中心;
- 论文关键词：间断Galerkin有限元 ; 网格结块 ; Newton-Krylov方法 ; 预处理方法
- 英文论文关键词：discontinuous Galerkin ; agglomeration ; Newton-Krylov method ; preconditioning
- 会议召开时间：2016-11-04
- 会议录名称：2016年度全国气动声学学术会议论文摘要集
- 语种：中文
- 分类号：O35;O241.82
- 学会代码：LTLX
- 会议名称：2016年度全国气动声学学术会议
- 会议地点：中国北京
- 主办单位：中国航空学会航空声学专业委员会、中国航空学会气动声学专业委员会、中国商飞上海飞机设计研究院、北京航空航天大学
- 学会名称：北京航空航天大学流体力学教育部重点实验室
- 页数：7
- 文件大小：537k
- 原文格式：D
- 会议级别：全国
摘要
基于间断Galerkin(DG)有限元格式发展了流场高精度数值求解方法。发展了网格结块方法保证稀疏网格上弯曲复杂外形的几何表达精度。研究了适用于DG格式的雅可比矩阵无关的Newton-Krylov(JFNK)方法,并对ILU预处理的JFNK-DG方法的内存和计算效率进行了测试。对复杂外形的流场进行了数值模拟,验证了间断Galerkin有限元方法的高精度特性及JFNK-DG方法的计算效率。
A high-order discontinuous galerkin(DG) method was developed to solve the three-dimensional Euler and Navier-Stokes equations.A Jacobian-free Newton-Krylov(JFNK) method is used and the Incomplete Lower Upper factorization(ILU) is adopted as a preconditioner.Storage requirement and computational efficiency are analyzed with the computation of flow past complex configurations.Numerical results indicate that highly accurate solutions and a high computational efficiency can be achieved with JFNK-DG method.
A high-order discontinuous galerkin(DG) method was developed to solve the three-dimensional Euler and Navier-Stokes equations.A Jacobian-free Newton-Krylov(JFNK) method is used and the Incomplete Lower Upper factorization(ILU) is adopted as a preconditioner.Storage requirement and computational efficiency are analyzed with the computation of flow past complex configurations.Numerical results indicate that highly accurate solutions and a high computational efficiency can be achieved with JFNK-DG method.
引文
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[6]秦望龙,吕宏强,伍贻兆.三维可压缩Navier-Stokes方程的间断Galerkin有限元方法研究法研究[J].空气动力学学报,即将发表..(QIN W L,Lu H Q,WU Y Z.Discontinuous Galerkin Method for 3-D compressible Navier-Stokes equations[J].ACTA Aerodynamica Sinica,unpublish.(in Chinese))
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[11]Hartmann R,Held J,Leicht T.Adjoint-based error estimation and adaptive mesh refinement for the RANS and k-ωturbulence model equations[J].Journal of Computational Physics,2011,230(11):4268-4284.
[12]Jiang ZH,Yan C,Yu J.Implicit high-order discontinuous Galerkin method with HWENO type limiters for steady viscous flow simulations.Acta Mechanica Sinica 2013;29(4),526-533.
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[15]http://www.as.dlr.de/hiocfd/case_c2.4.html
[16]Xia Yidong.A Parallel Implicit Reconstructed Discontinuous Galerkin Method for Compressible Flows on Hybrid Grids,Ph D thesis.North Carolina State:North Carolina State University,2013.
[2]Lu HQ,Sun Q,Qin WL.3D numerical solution of aeronoise with high-order discontinuous Galerkin method.Transactions of Nanjing University of Aeronautics&Astronautics 2013,30(3),227-231.
[3]Lu HQ,Xu YD,Gao YK,Sun Q,Qin WL.A CFD-based high-order Discontinuous Galerkin solver for three dimensional electromagnetic scattering problems.Advances in Engineering Software 2015;83,1-10.
[4]秦望龙,吕宏强,伍贻兆.基于混合网格的高阶间断有限元黏流数值解法[J].力学学报,2013,45(6):987-991.(Qin Wanglong,Lu Hongqiang,Wu yizhao.HIGH-ORDER DISCONTINUOUS GALERKINSOLUTION OF N-S EQUATIONS ON HYBRIDMESH[J].Chinese Journal of Theoretical and Applied Mechani,2013,45(6):987-991(in Chinese))
[5]秦望龙,吕宏强,伍贻兆.弯曲网格上的间断有限元湍流数值解法研究[J].空气动力学学报,2014,32(5):581-586.(QIN W L,Lu H Q,WU Y Z.Discontinuous galerkin solution of RANS equations on curved mesh[J].ACTA Aerodynamica Sinica,2014,32(5):581-586.(in Chinese))
[6]秦望龙,吕宏强,伍贻兆.三维可压缩Navier-Stokes方程的间断Galerkin有限元方法研究法研究[J].空气动力学学报,即将发表..(QIN W L,Lu H Q,WU Y Z.Discontinuous Galerkin Method for 3-D compressible Navier-Stokes equations[J].ACTA Aerodynamica Sinica,unpublish.(in Chinese))
[7]QIN Wanglong,LU Hongqiang,WU Yizhao,et al.Implicit discontinuous Galerkin method on agglomerated high order grids for three-dimensional simulations[J].Chinese Journal of Aeroacoustic.Unpublish.
[8]Cockburn B,Shu CW.The Runge-Kutta discontinuous Galerkin method for conservation laws V:multidimensional systems.J Comput Phys1997;141(2):199-224.
[9]Cockburn.B and C.Shu,The Runge-Kutta discontinuous Galerkin method for conservation laws V:multidimensional systems[J].Journal of Computational Physics,1998,141(2):199-224.
[10]Bassi F,Crivellini A,Rebay S,et al.Discontinuous Galerkin solution of the Reynolds-averaged NavierStokes and k-ωturbulence model equations[J].Computers&Fluids,2005,34(2):507-540.
[11]Hartmann R,Held J,Leicht T.Adjoint-based error estimation and adaptive mesh refinement for the RANS and k-ωturbulence model equations[J].Journal of Computational Physics,2011,230(11):4268-4284.
[12]Jiang ZH,Yan C,Yu J.Implicit high-order discontinuous Galerkin method with HWENO type limiters for steady viscous flow simulations.Acta Mechanica Sinica 2013;29(4),526-533.
[13]Xia Y,Luo H,Nourgaliev R.An implicit Hermite WENO reconstruction-based discontinuous Galerkin method on tetrahedral grids.Computers&Fluids2014;96(13),406-421.
[14]Xia Y,Luo H,Nourgaliev R.An Implicit Reconstructed Discontinuous Galerkin Method Based on Automatic Differentiation for the Compressible Flows on Tetrahedral Grids.2013.Report No.:AIAA-2013-0687.
[15]http://www.as.dlr.de/hiocfd/case_c2.4.html
[16]Xia Yidong.A Parallel Implicit Reconstructed Discontinuous Galerkin Method for Compressible Flows on Hybrid Grids,Ph D thesis.North Carolina State:North Carolina State University,2013.