Abstract
An implementation of a multigrid method in a three-dimensional SIMPLEC code based on a collocated grid arrangement is presented. The multigrid algorithm is FMG-FAS, using a V-cycle described by Brandt [1,2].
The coarse grid is obtained by merging eight fine grid cells in 3D, and four in 2D. Restriction and prolongation of field quantities are carried out by a weighted linear interpolation, and restriction of residuals by a summation. All variables and all equations, including the pressure correction equation, are treated in the same way.
To stabilize the solution process, a fraction of the multigrid sources is included in the diagonal coefficient a p , and a damping function is used on negative corrections of the turbulent quantities to prevent them from being negative.
The multigrid method was shown to be relative insensitive to the choice of under-relaxation parameters. Therefore 0.8 or 0.7 is used for all equations, except for the pressure correction equation where 1.5 is used.
Both turbulent and laminar calculations are presented for a 2D backward facing step, a 2D ventilated enclosure, and a 3D ventilated enclosure. The turbulent calculations are made with a two-layer low-Reynolds k − ε model. Different discretization schemes for the convective schemes are used including the first order hybrid scheme and two higher order schemes (QUICK and a van Leer TVD scheme).
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6 References
A. Brandt, Multi-level adaptive solutions to boundary-value problems. Math. of Comput., Vol.31 333–390 (1977)
A. Brandt, Multigrid techniques: 1984 guide with applications to fluid dynamics. Computational fluid dynamics lecture notes at von-Karman Institute, (1984)
G. J. Shaw and S. Sivaloganathan, On the smoothing properties of the SIMPLE pressure-correction algorithm, Int. J. Num. Meth. Fluids, Vol. 8, 441–461 (1988)
Y. Li, L. Fuchs S. Holmberg, An evaluation of a computer code for predicting indoor airflow and heat transfer., 12th AIVC Conf., Ottawa Canada (1991)
M. Perić, M. Rüger and G. Scheuerer, A finite volume multigrid method for calculating turbulent flows., Proc. 7th Symp. on Turb. Shear Flows, 7.3.1–7.3.6 Stanford, (1989)
F.S. Lien, M.A. Leschziner, Multigrid convergence accelleretion for complex flow including turbulence., Multigrid methods III Birkhäuser Verlag. (1991)
H.C. Chen V.C. Patel, Practical near-wall turbulence models for complex flows including separation., AIAA paper 87-1300, Honolulu (1987)
L. Davidson, B. Farhanieh, A finite volume code employing colocated variable arrangement and cartesian velocity components of fluid flow and heat transfer in complex three-dimensional geometries. Rept. 91/14 Dep. of Thermo-and Fluid Dyn., Chalmers Univ. of Techn. (1991)
S.V. Patankar, Numerical heat transfer and fluid flow, Hemispere Publishing Co., McGraw Hill, (1980)
C.M Rhie, W.L. Chow, Numerical study of the turbulent flow past an airfoil with trailing edge separation., AIAA J. Vol. 21, 1525–1532 (1983)
B.P. Leonard, A stable and accurate convective modelling procedure based on quadratic upstream interpolation Comput. Meth. in Appl. Mech and Eng. Vol. 19, 59–98 (1979)
B. Van Leer, Towards the ultimate conservation difference scheme. II. Monotonocity and conservation combined in a second-order scheme J. of Comput. Phys. Vol. 14, 361–370 1974
P. Johansson, A three-dimensional laminar multigrid method applied to the SIMLEC algorithm, Diploma Thesis, Rept. 92/5 Dep. of Thermo-and Fluid Dyn., Chalmers Univ. of Techn. (1992)
T. Hellström, Davidson L., A multiblock-moving mesh extension to the CALC-BFC code. Rept. 93/3 Dep. of Thermo-and Fluid Dyn.,Chalmers Univ. of Techn. (1993)
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© 1994 Springer Basel AG
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Johansson, P., Davidson, L. (1994). A Full Multigrid Method Applied to Turbulent Flow using the SIMPLEC Algorithm Together with a Collocated Arrangement. In: Hemker, P.W., Wesseling, P. (eds) Multigrid Methods IV. ISNM International Series of Numerical Mathematics, vol 116. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8524-9_18
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DOI: https://doi.org/10.1007/978-3-0348-8524-9_18
Publisher Name: Birkhäuser, Basel
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