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Finite volume multigrid prediction of laminar natural convection: Bench- mark solutions. (English) Zbl 0711.76072
Summary: A finite volume multigrid procedure for the prediction of laminar natural convection flows is presented, enabling efficient and accurate calculations on very fine grids. The method is fully conservative and uses second-order central differencing for convection and diffusion fluxes. The calculations start on a coarse (typically 10\(\times 10\) control volumes) grid and proceed to finer grids until the desired accuracy or maximum affordable storage is reached. The computing times increase thereby linearly with the number of control volumes. Solutions are presented for the flow in a closed cavity with side walls at different temperatures and insulated top and bottom walls. Rayleigh numbers of \(10^ 4\), \(10^ 5\) and \(10^ 6\) are considered. Grids as fine as 640\(\times 640\) control volumes are used and the results are believed to be accurate to within 0.01%. Second-order monotonic convergence to grid-independent values is observed for all predicted quantities.

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76R10 Free convection
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[1] de Vahl Davis, Int. j. numer. methods fluids 3 pp 249– (1983)
[2] ’Multi-level adaptive computations in fluid dynamics’, AIAA Paper 79-1455, 1979.
[3] Vanka, J. Comput. Phys. 65 pp 138– (1986)
[4] Sivaloganathan, Int. j. numer. methods fluids 8 pp 417– (1988)
[5] Dick, Int. J. numer. methods fluids 9 pp 113– (1989)
[6] and , ’A control volume based full multigrid procedure for the prediction of two-dimensional, laminar, incompressible flows’, in (ed.), Notes on Numerical Fluid Mechanics, Vol. 20, Vieweg, Braunschweig, 1988, pp. 9-16.
[7] , and , ’Finite volume multigrid solutions of the two-dimensional incompressible Navier-Stokes equations’, in ! (ed.), Notes on Numerical Fluid Mechanics, Vol. 23, Vieweg, Braunschweig, 1988, pp. 37-47.
[8] and , ’A finite volume multigrid method for calculating turbulent flows’, Proc. 7th Symp. on Turbulent Shear Flows, Stanford, CA, 1989, pp. 7.3.1-7.3.6.
[9] de Vahl Davis, Int. j. numer. methods fluids 3 pp 227– (1983)
[10] Perić, Comput. Fluids 16 pp 389– (1988)
[11] Khosla, Comput. Fluids 2 pp 207– (1974)
[12] Stone, SIAM J. Numer. Anal. 5 pp 530– (1968)
[13] Patankar, Int. J. Heat Mass Transfer 15 pp 1787– (1972)
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