Multigrid method based on the transformation-free HOC scheme on nonuniform grids for 2D convection diffusion problems

被引:44
作者
Ge, Yongbin [1 ]
Cao, Fujun [2 ]
机构
[1] Ningxia Univ, Inst Appl Math & Mech, Ningxia 750021, Peoples R China
[2] Inner Mongolia Univ Sci & Technol, Sch Math Phys & Biol Engn, Baotou, Inner Mongolia, Peoples R China
基金
中国国家自然科学基金;
关键词
Convection diffusion equation; Nonuniform grids; Multigrid method; Boundary layer; Local singularity; Navier-Stokes equations; Stream function-vorticity formulation; NAVIER-STOKES EQUATIONS; MESH REFINEMENT PROCEDURE; ORDER COMPACT SCHEME; ITERATIVE SOLUTION; DIFFERENCE SCHEME; STEADY; ACCURACY; SOLVER; FLOW;
D O I
10.1016/j.jcp.2011.02.027
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
In this paper, a multigrid method based on the high order compact (HOC) difference scheme on nonuniform grids, which has been proposed by Kalita et al. [J.C. Kalita, A.K. Dass, D.C. Dalal, A transformation-free HOC scheme for steady convection-diffusion on nonuniform grids, Int. J. Numer. Methods Fluids 44 (2004) 33-53], is proposed to solve the two-dimensional (2D) convection diffusion equation. The HOC scheme is not involved in any grid transformation to map the nonuniform grids to uniform grids, consequently, the multigrid method is brand-new for solving the discrete system arising from the difference equation on nonuniform grids. The corresponding multigrid projection and interpolation operators are constructed by the area ratio. Some boundary layer and local singularity problems are used to demonstrate the superiority of the present method. Numerical results show that the multigrid method with the HOC scheme on nonuniform grids almost gets as equally efficient convergence rate as on uniform grids and the computed solution on nonuniform grids retains fourth order accuracy while on uniform grids just gets very poor solution for very steep boundary layer or high local singularity problems. The present method is also applied to solve the 2D incompressible Navier-Stokes equations using the stream function-vorticity formulation and the numerical solutions of the lid-driven cavity flow problem are obtained and compared with solutions available in the literature. (C) 2011 Elsevier Inc. All rights reserved.
引用
收藏
页码:4051 / 4070
页数:20
相关论文
共 47 条
[1]   A conservative adaptive projection method for the variable density incompressible Navier-Stokes equations [J].
Almgren, AS ;
Bell, JB ;
Colella, P ;
Howell, LH ;
Welcome, ML .
JOURNAL OF COMPUTATIONAL PHYSICS, 1998, 142 (01) :1-46
[2]   LOCAL ADAPTIVE MESH REFINEMENT FOR SHOCK HYDRODYNAMICS [J].
BERGER, MJ ;
COLELLA, P .
JOURNAL OF COMPUTATIONAL PHYSICS, 1989, 82 (01) :64-84
[3]   AN EFFICIENT SCHEME FOR SOLVING STEADY INCOMPRESSIBLE NAVIER-STOKES EQUATIONS [J].
BRUNEAU, CH ;
JOURON, C .
JOURNAL OF COMPUTATIONAL PHYSICS, 1990, 89 (02) :389-413
[4]   A PERTURBATIONAL H4 EXPONENTIAL FINITE-DIFFERENCE SCHEME FOR THE CONVECTIVE DIFFUSION EQUATION [J].
CHEN, GQ ;
GAO, Z ;
YANG, ZF .
JOURNAL OF COMPUTATIONAL PHYSICS, 1993, 104 (01) :129-139
[5]   A HIGH-ORDER DIFFERENCE METHOD FOR THE STEADY-STATE NAVIER-STOKES EQUATIONS [J].
CHOO, JY ;
SCHULTZ, DH .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1994, 27 (11) :105-119
[6]   HIGH-ORDER METHODS FOR DIFFERENTIAL-EQUATIONS WITH LARGE 1ST-DERIVATIVE TERMS [J].
DEKEMA, SK ;
SCHULTZ, DH .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 1990, 10 (03) :259-284
[7]   COMPACT H-4 FINITE-DIFFERENCE APPROXIMATIONS TO OPERATORS OF NAVIER STOKES TYPE [J].
DENNIS, SCR ;
HUDSON, JD .
JOURNAL OF COMPUTATIONAL PHYSICS, 1989, 85 (02) :390-416
[8]   Fourth-order compact formulation of Navier-Stokes equations and driven cavity flow at high Reynolds numbers [J].
Erturk, E ;
Gökçöl, C .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 2006, 50 (04) :421-436
[9]  
Farrell P., 2000, Robust Computational Techniques for Boundary Layers
[10]   High accuracy iterative solution of convection diffusion equation with boundary layers on nonuniform grids [J].
Ge, LX ;
Zhang, J .
JOURNAL OF COMPUTATIONAL PHYSICS, 2001, 171 (02) :560-578