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

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

淮北师范大学数学科学学院, 安徽淮北 235000

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
计量
- 文章访问数: 1595
- HTML全文浏览量: 272
- PDF下载量: 341
- 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

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

School of Mathematical Science, Huaibei Normal University,Huaibei, Anhui 235000, P.R.China

摘要

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.
- Navier-Stokes方程 /
- 间断有限元方法 /
- 黏性流体
Abstract: The incompressible Navier-Stokes equations are composed of the conservation law and the diffusion and constrained development equations. To test the numerical method, based on the unstructured grid, a discontinuous Galerkin scheme was established. The numerical results of the eddy current problem for different viscosity coefficients υ were discussed. The simulation results show that, the method has high precision and can solve the incompressible viscous fluid problem with moving interface, which makes the simulation boundary layer, the shear layer and the complex vortex solution be very effective, and the shock structure can be successfully extended to the numerical simulation of complex phenomena.
- Navier-Stokes equation /
- discontinuous Galerkin finite element method /
- viscous flow

HTML全文

参考文献(16)

[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.

施引文献

资源附件(0)

访问统计

计量

文章访问数: 1595
HTML全文浏览量: 272
PDF下载量: 341
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

留言板

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

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).

计量

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

计量

目录

留言板

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

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).

计量

出版历程

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

计量

出版历程

目录

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).