Moving Mesh Finite Element Method for Unsteady Navier-Stokes Flow

被引：2

作者：

Wu, Yirong ^{[1
]}

Wang, Heyu ^{[1
]}

机构：

[1] Zhejiang Univ, Sch Math Sci, Hangzhou 310027, Zhejiang, Peoples R China

来源：

ADVANCES IN APPLIED MATHEMATICS AND MECHANICS | 2017年 / 9卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Navier-Stokes system; 4P(1) - P-1; hierarchy geometry tree; moving mesh method; HARMONIC MAPS; STABILIZATION; EQUATIONS;

D O I：

10.4208/aamm.2016.m1457

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we use moving mesh finite element method based upon 4P(1) - P-1 element to solve the time-dependent Navier-Stokes equations in 2D. Two-layer nested meshes are used including velocity mesh and pressure mesh, and velocity mesh can be obtained by globally refining pressure mesh. We use hierarchy geometry tree to store the nested meshes. This data structure make convienence for adaptive mesh method and the construction of multigrid preconditioning. Several numerical problems are used to show the effect of moving mesh.

引用

页码：742 / 756

页数：15

共 21 条

[1]

[Anonymous], 2005, FINITE ELEMENTS FAST

[2] ERROR ESTIMATES FOR FINITE-ELEMENT METHOD SOLUTION OF THE STOKES PROBLEM IN THE PRIMITIVE VARIABLES [J].

BERCOVIER, M ;

PIRONNEAU, O .

NUMERISCHE MATHEMATIK, 1979, 33 (02) :211-224

[3] Space-time adaptive simulations for unsteady Navier-Stokes problems [J].

Berrone, S. ;

Marro, M. .

COMPUTERS & FLUIDS, 2009, 38 (06) :1132-1144

[4] Stabilization of low-order mixed finite elements for the Stokes equations [J].

Bochev, PB ;

Dohrmann, CR ;

Gunzburger, MD .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2006, 44 (01) :82-101

[5] An r-adaptive finite element method based upon moving mesh PDEs [J].

Cao, WM ;

Huang, WZ ;

Russell, RD .

JOURNAL OF COMPUTATIONAL PHYSICS, 1999, 149 (02) :221-244

[6] A Newton method with adaptive finite elements for solving phase-change problems with natural convection [J].

Danaila, Ionut ;

Moglan, Raluca ;

Hecht, Frederic ;

Le Masson, Stephane .

JOURNAL OF COMPUTATIONAL PHYSICS, 2014, 274 :826-840

[7] Moving mesh finite element methods for the incompressible Navier-Stokes equations [J].

Di, Y ;

Li, R ;

Tang, T ;

Zhang, PW .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2005, 26 (03) :1036-1056

[8] ADAPTIVE GRID GENERATION FROM HARMONIC MAPS ON RIEMANNIAN-MANIFOLDS [J].

DVINSKY, AS .

JOURNAL OF COMPUTATIONAL PHYSICS, 1991, 95 (02) :450-476

[9]

EBEDIA M. S., 2009, 47 AIAA AER SCI M OR

[10]

Fujima S., 1998, CONTEMP MATH, V218, P246

← 1 2 3 →