Abstract
This paper describes an efficient line solver for the coupled equations. The calculation procedure, called SCGS/LS(Symmetrical Coupled Gauss-Seidel/Line Solver), is based on the SCGS scheme. The technique is applied to the driven cavity problem for the incompressible Navier-Stokes equations. A Fourier analysis of this technique is carried out. The scheme is simple and easy to programme. The rates of convergence and the computational times are reported for the test case.
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References
A. Brandt. Guide to multigrid development. Lecture Notes in Mathematics,(960), 1981. Springer Verlag.
P. H. Gaskell and N. G. Wright. Multigrids applied to an efficient fully coupled solution technique for Recirculating fluid flow problems. In Simul. and Optimisation of large System. IMA, IMA, september 1986.
K. N. Ghia, U. Ghia and C. T. Shin. High-Re solution for incompressible flow using the Navier-Stokes equations and a multigrid method. J. Comput. Phys., (48): 387–411, 1982.
F. H. Harlow and J. E. Welch. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. The Physics of Fluids, 8 (12), December 1965.
T. M. Shah. Analysis of a multigrid method. Master’s thesis, Oxford University, Oxford University computing Laboratory, 1987.
G. J. Shaw and S. Sivaloganathan. On the smoothing properties of the SIMPLE pressure correction algorithm. Inter. J. Num. Methods for Fluids, 8: 441–462, 1988.
S. Sivaloganathan G. J. Shaw T. M. Shah and D. F. Mayers A comparison of multigrid methods for the incompressible Navier-Stokes equations. In K. W. Morton and M. J. Baines, editors, Numerical Methods for Fluid Dynamics. Oxford University Press, March 1988.
S. Sivaloganathan and G. J. Shaw. A multigrid method for Recirculating flows. Inter. J. Num. Methods for Fluids, 8: 417–440, 1988.
K. Stuben and U. Trottenberg. Multigrid methods: Fundamental algorithms, model problem analysis and application. Lecture Notes in Mathematics, (960): 1–176, 1981.
S. P. Vanka. Block implicit multigrid calculation of two-dimensional Recirculating flows. Comput. Meths. Appl. Mech. Engrg., (59): 29–48, 1986.
S. P. Vanka. Block implicit multigrid solution of the Navier-Stokes equations in primitive variables. J. Comput. Phys., (65): 138–158, 1986.
S. P. Vanka. A calculation procedure for three-dimensional steady Recirculating flows using multigrid methods. Comput. Meths. Appl. Mech. Engrg., (55): 321–338, 1986.
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© 1990 Springer Fachmedien Wiesbaden
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Shah, T.M., Mayers, D.F., Rollett, J.S. (1990). Analysis and Application of A Line Solver for the Recirculating Flows Using Multigrid Methods. In: Hackbusch, W., Rannacher, R. (eds) Numerical Treatment of the Navier-Stokes Equations. Notes on Numerical Fluid Mechanics (NNFM), vol 30 5. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-14004-7_13
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DOI: https://doi.org/10.1007/978-3-663-14004-7_13
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-528-07630-6
Online ISBN: 978-3-663-14004-7
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