A multigrid method for recirculating flows

The use of multigrid methods in complex fluid flow problems is recent and still under development. In this paper we present a multigrid method for the incompressible Navier-Stokes equations. The distinctive features of the method are the use of a pressure-correction method as a smoother and a novel continuity-preserving manner of grid coarsening. The shear-driven cavity problem is used as a test case to demonstrate the efficiency of the method.

[1]  P. Wesseling A robust and efficient multigrid method , 1982 .

[2]  A. Brandt Guide to multigrid development , 1982 .

[3]  M. D. Olson,et al.  Review of computing methods for recirculating flows , 1978 .

[4]  N. Bakhvalov On the convergence of a relaxation method with natural constraints on the elliptic operator , 1966 .

[5]  D. Brandt,et al.  Multi-level adaptive solutions to boundary-value problems math comptr , 1977 .

[6]  Robert L. Street,et al.  Visualization Studies of a Shear Driven Three-Dimensional Recirculating Flow , 1984 .

[7]  R. P. Fedorenko A relaxation method for solving elliptic difference equations , 1962 .

[8]  Robert L. Lee,et al.  A MODIFIED FINITE ELEMENT METHOD FOR SOLVING THE TIME-DEPENDENT, INCOMPRESSIBLE NAVIER-STOKES EQUATIONS. PART 1: THEORY* , 1984 .

[9]  S. Vanka Block-implicit multigrid solution of Navier-Stokes equations in primitive variables , 1986 .

[10]  Laszlo Fuchs,et al.  Solution of three‐dimensional viscous incompressible flows by a multi‐grid method , 1984 .

[11]  D. Spalding,et al.  A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows , 1972 .

[12]  Suhas V. Patankar,et al.  A Calculation Procedure for Two-Dimensional Elliptic Situations , 1981 .

[13]  A. Acrivos,et al.  Steady flows in rectangular cavities , 1967, Journal of Fluid Mechanics.

[14]  U. Ghia,et al.  High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method , 1982 .

[15]  J. Strikwerda Upwind Differencing, False Scaling, and Nonphysical Solutions to the Driven Cavity Problem , 1981 .