不可压缩黏性流体的二维Navier-Stokes方程的间断有限元模拟  

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

作　　者：陈亚飞 郑云英[1] CHEN Yafei;ZHENG Yunying(School of Mathematical Science,Huaibei Normal University,Huaibei,Anhui 235000,P.R.China)

机构地区：[1]淮北师范大学数学科学学院,安徽淮北235000

出　　处：《应用数学和力学》2020年第8期844-852,共9页Applied Mathematics and Mechanics

基　　金：安徽省高校自然科学研究重大项目(KJ2018A0385)。

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.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 coefficientsνwere 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.

关 键 词：NAVIER-STOKES方程 间断有限元方法 黏性流体 

分 类 号：O241.82[理学—计算数学]