Abstract
This paper presents a full multigrid solver for the simulation of a flow over a yawed flat plate. The two problems associated with this simulation; boundary layers and entering flows with non-aligned characteristics, have been successfully overcome through the combination of a plane-implicit solver and semicoarsening. In fact, this multigrid algorithm exhibits a textbook multigrid convergence rate, i.e., the solution of the discrete system of equations is obtained in a fixed amount of computational work, independently of the grid size, grid stretching factor and non-alignment parameter. Also, a parallel variant of the smoother based on a four-color ordering of planes is investigated.
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REFERENCES
Brandt, A. (1984). Multigrid techniques: 1984 guide with applications to fluid dynamics. Technical Report GMD-Studien 85, GMD.
Brandt, A. (1998). Barriers to Achieving Textbook Multigrid Efficiency (TME) in CFD, ICASE Interim Report No. 32.
Dendy, J. E., McCormick, S. F., Ruge, J. W., Russell, T. F., and Schaffer, S. (1989). Multigrid methods for three-dimensional petroleum reservoir simulation. In Tenth SPE Symposium on Reservoir Simulation.
Diskin, B. (1997). Multigrid algorithm with conditional coarsening for the nonaligned sonic flow. Proceedings of the Eighth Copper Mountain Conference on Multigrid Methods, Electronic Trans. Num. An., Vol. 6, pp. 106–119.
Goldstein, S. (1933). On the two-dimensional steady flow of a viscous fluid behind a solid body. Proc. Roy. Soc. London Ser. A, 545–573.
Hayase, T., Humphrey, J. A. C., and Greif, R. (1992). A Consistently Formulated QUICK scheme for fast and stable convergence using finite-volume iterative calculation procedures. Comput. Phys. 98, 108–118.
Llorente, I. M., and Melson, N. D. (2000). Behavior of plane relaxation methods as multigrid smoothers. Electron. Trans. Numer. Anal. 10, 92–114
Llorente, I. M., Prieto-Matias, M., and Diskin, B. An efficient parallel multigrid solver for 3-D convection-dominated problems. Technical Report 2000–29, ICASE, to appear in Parallel Computing.
Montero, R. S., and Llorente, I. M. Robust multigrid algorithms for the incompresible Navier–Stokes equations. Technical Report 00–27, ICASE, 2000, to appear in J. of Comp. Phys.
Prieto, M., Montero, R. S., Espadas, D., Llorente, I. M., and Tirado, F. (2001). Parallel multigrid for anisotropic elliptic equations. J. Parallel Distr. Com. 61, 96–114.
Thomas, J. L., Diskin, B., and Brandt, A. (1999). Textbook multigrid efficiency for the incompressible Navier–Stokes equations: High Reynolds number wakes and boundary layers. Technical Report 99–51, ICASE.
Vanka, S. P. (1986). Block-implicit multigrid solution of Navier–Stokes equations in primitive variables. Comput. Phys. 65, 138–158
Washio, T., and Oosterlee, K. (1998). Flexible multiple semicoarsening for three-dimensional singularly perturbed problems. SIAM J. Sci. Comput. 19, 1646–1666.
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Montero, R.S., Llorente, I.M. & Salas, M.D. A Robust Multigrid Algorithm for the Simulation of a Yawed Flat Plate. Journal of Scientific Computing 17, 481–490 (2002). https://doi.org/10.1023/A:1015154126334
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DOI: https://doi.org/10.1023/A:1015154126334