Optimal multigrid solutions of two-dimensional convection-conduction problems. (English) Zbl 1077.65508

Mesquita, Maximilian S.; de Lemos, Marcelo J. S.

Appl. Math. Comput. 152, No. 3, 725-742 (2004).

Summary: The present work investigates the efficiency of the multigrid numerical method when used to solve two-dimensional laminar velocity and temperature fields inside a rectangular domain. Numerical analysis is based on the finite volume discretization scheme applied to structured orthogonal regular meshes. Performance of the correction storage (CS) multigrid algorithm is compared for different inlet Reynolds number \((Re_{in})\) and number of grids. Up to four grids were used for both \(V\)- and \(W\)-cycles. Simultaneous and uncoupled temperature-velocity solution schemes were investigated. Advantages in using more than one grid are discussed. For simultaneous solution, results further indicate an increase in the computational effort for higher inlet Reynolds number Rein. Optimal number of intermediate relaxation sweeps for within both \(V\)- and \(W\)-cycles is discussed upon.

MSC:

65N55	Multigrid methods; domain decomposition for boundary value problems involving PDEs
76M25	Other numerical methods (fluid mechanics) (MSC2010)

Keywords:

Multigrid; Numerical methods; CFD; Laminar flow; Decoupled solution

References:

[1]	Brandt, A., Multi-level adaptive solutions to boundary-value problems, Math. comp., 31, 138, 333-390, (1977) · Zbl 0373.65054
[2]	Hackbusch, W., Multigrid methods and applications, (1985), Springer-Verlag Berlin · Zbl 0577.65118
[3]	Hortmann, M.; Peric, M.; Scheuerer, G., Finite volume multigrid prediction of laminar convection: bench-mark solutions, Int. J. numer. meth. fluids, 11, 189-207, (1990) · Zbl 0711.76072
[4]	Hutchinson, B.R.; Galpin, P.F.; Raithby, G.D., Application of additive correction multigrid to the coupled fluid flow equations, Numer. heat transfer, 13, 133-147, (1988) · Zbl 0642.76053
[5]	Jiang, Y.; Chen, C.P.; Tucker, P.K., Multigrid solutions of unsteady navier – stokes equations using a pressure method, Numer. heat transfer–part A, 20, 81-93, (1991)
[6]	Patankar, S.V., Numerical heat transfer and fluid flow, (1980), Mc-Graw Hill · Zbl 0595.76001
[7]	M. Peric, M. Rüger, G. Scheuerer, A finite volume multigrid method for calculating turbulent flows, in: Seventh Symposium on Turbulent Shear Flows, Standford University, 1989, pp. 7.3.1-7.3.6
[8]	J.A. Rabi, M.J.S. de Lemos, Multigrid numerical solution of incompressible laminar recirculating flows, in: ENCIT98- Proc. 7th Braz. Cong. Eng. Th. Sci., vol. 2, Rio de Janeiro, RJ, 3-6 November 1998, pp. 915-920
[9]	J.A. Rabi, M.J.S. de Lemos, The effects of peclet number and cycling strategy on multigrid numerical solutions of convective – conductive problems, in: 7th AIAA/ASME Joint Thermophysics and Heat Transfer Conf., Albuquerque, New Mexico, USA, 15-18 June 1998, Paper AIAA-98-2584
[10]	Rabi, J.A.; de Lemos, M.J.S., Optimization of convergence acceleration in multigrid numerical solutions of conductive – convective problems, Appl. math. comput., 124, 215-226, (2001) · Zbl 1024.65103
[11]	J.A. Rabi, M.J.S. de Lemos, Multigrid correction-storage formulation applied to the numerical solution of incompressible laminar recirculating flows, Appl. Math. Modelling (in press) · Zbl 1106.76426
[12]	Sathyamurthy, P.S.; Patankar, S.V., Block-correction-based multigrid method for fluid flow problems, Numer. heat transfer - part B, 25, 375-394, (1994)
[13]	Stüben, K.; Trottenberg, U., Multigrid methods, (), 1-76