Multigrid methods to accelerate convergence of element-by-element solution algorithms for viscous incompressible flows

M.P. Reddy1, J.N. Reddy2
1The Computational Mechanics Company Inc., Austin, TX 78752, USA
2Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843, USA

Tài liệu tham khảo

Carey, 1984 Hestenes, 1952, Methods of conjugate gradients for solving linear systems, Nat. Bur. Std. J. Res., 49, 409, 10.6028/jres.049.044 Golub, 1989 Jea, 1983, On simplification of generalized conjugate gradient methods for nonsymmetrizable linear systems, Linear Algebra Appl., 52, 399, 10.1016/0024-3795(83)80026-3 Fox, 1968, Developments in structural analysis by direct energy minimization, AIAA J., 6, 1036, 10.2514/3.4670 Fried, 1970, A gradient computational procedure for the solution of large problems arising from the finite element discretization method, Int. J. Numer. Methods Engrg., 2, 477, 10.1002/nme.1620020403 Saad, 1986, GMRES: A generalized minimum residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Comput., 7, 856, 10.1137/0907058 Hayes, 1989, Advances and trends in element-by-element techniques, 219 Wathen, 1989, An analysis of some element-by-element techniques, Comput. Methods Appl. Mech. Engrg., 74, 217, 10.1016/0045-7825(89)90052-2 Hughes, 1983, An element-by-element solution algorithm for problems of structural and solid mechanics, Comput. Methods Appl. Mech. Engrg., 36, 241, 10.1016/0045-7825(83)90115-9 Hughes, 1987, Large-scale vectorized implicit calculations in solid mechanics on a Cray X-MP/48 utilizing EBE preconditioned conjugate gradients, Comput. Methods Appl. Mech. Engrg., 61, 215, 10.1016/0045-7825(87)90005-3 Winget, 1985, Solution algorithms for nonlinear transient heat conduction analysis employing element-by-element iterative strategies, Comput. Methods Appl. Mech. Engrg., 52, 711, 10.1016/0045-7825(85)90015-5 Carey, 1984, Subcritical flow computations using element-by-element conjugate gradient method, 103 Carey, 1986, Element-by-element linear and nonlinear solution schemes, Comm. Appl. Numer. Methods, 2, 281, 10.1002/cnm.1630020309 Shakib, 1989, A multi-element group preconditioned GMRES algorithm for nonsymmetric systems arising in finite element analysis, Comput. Methods Appl. Mech. Engrg., 75, 415, 10.1016/0045-7825(89)90040-6 Tezduyar, 1988, Element-by-element and implicit-explicit finite element formulations for computational fluid dynamics, 281 Tezduyar, 1989, Grouped element-by-element iteration schemes for incompressible flow computations, Comput. Phys. Comm., 53, 441, 10.1016/0010-4655(89)90177-X Reddy, 1992, Penalty-finite element analysis of incompressible flows using element-by-element solution algorithms, Comput. Methods Appl. Mech. Engrg., 100, 169, 10.1016/0045-7825(92)90182-J Reddy, 1992, Numerical simulation of forming processes using a coupled fluid flow and heat transfer model, Int. J. Numer. Methods Engrg., 35, 807, 10.1002/nme.1620350411 Salonen, 1985, A pressure determination scheme, 128 Shiojima, 1989, A pressure-smoothing scheme for incompressible flow problems, Int. J. Numer. Methods Fluids, 9, 557, 10.1002/fld.1650090506 Reddy, 1993, Accuracy and convergence of element-by-element iterative solvers for incompressible fluid flows using penalty finite element method, Int. J. Numer. Methods Fluids, 17, 1019, 10.1002/fld.1650171202 Brandt, 1977, Multi-level adaptive solutions to boundary-value problems, Math. Comput., 31, 333, 10.1090/S0025-5718-1977-0431719-X Brandt, 1981, Guide to multigrid development, 220 Reddy, 1994 Reddy, 1982, On penalty function methods in the finite element analysis of fluid flow, Int. J. Numer. Methods Engrg., 2, 151, 10.1002/fld.1650020204 Reddy, 1982, Penalty-finite-element analysis of 3-D Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg., 35, 87, 10.1016/0045-7825(82)90034-2 Reddy, 1986 Reddy, 1992 Lee, 1979, Smoothing techniques for certain primitive variable solutions of the Navier-Stokes equations, Int. J. Numer. Methods Engrg., 14, 1785, 10.1002/nme.1620141204