留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

不可压缩黏性流体的二维Navier-Stokes方程的间断有限元模拟

陈亚飞 郑云英

陈亚飞, 郑云英. 不可压缩黏性流体的二维Navier-Stokes方程的间断有限元模拟[J]. 应用数学和力学, 2020, 41(8): 844-852. doi: 10.21656/1000-0887.400379
引用本文: 陈亚飞, 郑云英. 不可压缩黏性流体的二维Navier-Stokes方程的间断有限元模拟[J]. 应用数学和力学, 2020, 41(8): 844-852. doi: 10.21656/1000-0887.400379
CHEN Yafei, ZHENG Yunying. A Discontinuous Galerkin FEM for 2D Navier-Stokes Equations of Incompressible Viscous Fluids[J]. Applied Mathematics and Mechanics, 2020, 41(8): 844-852. doi: 10.21656/1000-0887.400379
Citation: CHEN Yafei, ZHENG Yunying. A Discontinuous Galerkin FEM for 2D Navier-Stokes Equations of Incompressible Viscous Fluids[J]. Applied Mathematics and Mechanics, 2020, 41(8): 844-852. doi: 10.21656/1000-0887.400379

不可压缩黏性流体的二维Navier-Stokes方程的间断有限元模拟

doi: 10.21656/1000-0887.400379
基金项目: 安徽省高校自然科学研究重大项目(KJ2018A0385)
详细信息
    作者简介:

    陈亚飞(1992— ),女,硕士生(E-mail: 610556349@qq.com);郑云英(1973— ),女,教授,博士(通讯作者. E-mail: zhengyunying@eyou.com).

  • 中图分类号: O241.82

A Discontinuous Galerkin FEM for 2D Navier-Stokes Equations of Incompressible Viscous Fluids

  • 摘要: 由于不可压缩Navier-Stokes方程由守恒律、扩散及约束发展方程混合构成,为测试数值方法,该文基于非结构网格,对该方程建立了DG(discontinuous Galerkin)格式,讨论了不同黏性系数ν在方腔涡流问题的数值结果,验证了该方法的有效性且不依赖于问题的维数.圆柱绕流问题的模拟结果进一步表明此方法精度高、可有效求解具有运动界面的不可压缩黏性流体问题,使得模拟边界层、剪切层及复杂涡流解十分有效,并可以成功地推广到解决复杂现象数值模拟中的激波结构.
  • [1] 曹伟. 黏性不可压缩流体流动前沿的数值模拟[J]. 力学学报, 2004,〖STHZ〗 36(5): 583-588.(CAO Wei. Numerical simulation for the flow front of viscous incompressible fluid[J]. Chinese Journal of Theoretical and Applied Mechanics,2004, 36(5): 583-588.(in Chinese))
    [2] NAGRATH S, JANSEN K E, JR LAHEY R T. Computation of incompressible bubble dynamics with a stabilized finite element level set method[J]. Computer Methods in Applied Mechanics and Engineering,2005,194(42/44): 4565-4587.
    [3] 马飞遥, 马逸尘, 沃维丰. 基于二重网格的定常Navier-Stokes方程的局部和并行有限元算法[J]. 应用数学和力学, 2007,28(1): 25-33.(MA Feiyao, MA Yichen,WO Weifeng. Local and parallel finite element algorithms based on two-grid discretization for steady Navier-Stokes equations[J]. Applied Mathematics and Mechanics,2007,28(1): 25-33.(in Chinese))
    [4] 骆艳, 冯民富. 可压缩Navier-Stokes方程的压力梯度局部投影间断有限元法[J]. 应用数学和力学, 2008,〖STHZ〗 29(2): 157-168.(LUO Yan, FENG Minfu. Discontinuous element pressure gradient stabilizations for the compressible Navier-Stokes equations based on local projections[J]. Applied Mathematics and Mechanics,2008,29(2): 157-168.(in Chinese))
    [5] CHO M H, CHOI H G, YOO J Y. A direct reinitialization approach of level-set/splitting finite element method for simulating incompressible two-phase flows[J]. International Journal for Numerical Methods in Fluids,2011,67(11): 1637-1654.
    [6] HEIMANN F, ENGWER C, IPPISCH O, et al. An unfitted interior penalty discontinuous Galerkin method for incompressible Navier-Stokes two-phase flow[J]. International Journal for Numerical Methods in Fluids,2013,71(3): 269-293.
    [7] 章争荣. 不可压缩黏性流动N-S方程直接耦合数值求解的流形方法[C]//中国力学大会: 2013论文摘要集. 西安, 2013.(ZHANG Zhengrong. Manifold method for directly coupled numerical solution of N-S equations of incompressible viscous flow [C]// China Mechanics Conference: 2013 Abstracts.Xi’an, 2013.(in Chinese))
    [8] 郭虹平, 欧阳洁. 气液两相流的间断有限元模拟[J]. 计算物理, 2015,32(2): 160-168.(GUO Hongping, OUYANG Jie. Simulation of gas-liquid two-phase flows with discontinuous Galerkin method[J]. Chinese Journal of Computational Physics,2015,32(2): 160-168.(in Chinese))
    [9] 秦望龙, 吕宏强, 伍贻兆, 等. 三维可压缩Navier-Stokes方程的间断Galerkin有限元方法研究[J]. 空气动力学学报, 2016,34(5): 617-624.(QIN Wanglong, Lü Hongqiang, WU Yizhao, et al. Discontinuous Galerkin method for 3-D compressible Navier-Stokes equations[J]. Acta Aerodynamica Sinica,2016,34(5): 617-624.(in Chinese))
    [10] AMROUCHE C, ESCOBEDO M, Ghosh A. Semigroup theory for the Stokes operator with Navier boundary condition on spaces[J]. Archive for Rational Mechanics & Analysis,2018,223(2): 1-60.
    [11] KIRK K, RHEBERGEN S. Analysis of a pressure-robust hybridized discontinuous Galerkin method for the stationary Navier-Stokes equations[J]. Journal of Scientific Computing,2019,81(2): 881-897.
    [12] KARNIADAKIS G E, ISRAELI M, ORSZAG S A. High-order splitting methods for the incompressible Navier-Stokes equations[J]. Journal of Computational Physics,1991,97(2): 414-443.
    [13] YACOUBI A E, XU S, WANG Z J. A new method for computing particle collisions in Navier-Stokes flows[J]. Journal of Computational Physics,2019,399: 108919.
    [14] PAL S, HALOI R. On solution to the Navier-Stokes equations with Navier slip boundary condition for three dimensional incompressible fluid[J]. Acta Mathematica Scientia,2019,39(6): 1628-1638.
    [15] SHAHBAZI K, FISCHER P F, ETHIER C R. A high-order discontinuous Galerkin method for the unsteady incompressible Navier-Stokes equations[J]. Journal of Computational Physics,2007,222(1): 391-407.
    [16] JOHN V. Reference values for drag and lift of a two-dimensional time-dependent flow around a cylinder[J]. International Journal for Numerical Methods in Fluids,2010,44(7): 777-788.
  • 加载中
计量
  • 文章访问数:  733
  • HTML全文浏览量:  65
  • PDF下载量:  326
  • 被引次数: 0
出版历程
  • 收稿日期:  2019-12-24
  • 修回日期:  2020-06-29
  • 刊出日期:  2020-08-01

目录

    /

    返回文章
    返回