Abstract
The application of linear multigrid methods in conjunction with Krylov subspace methods on unstructured grids for two- and three-dimensional problems is shown. Also the use of such methods on hybrid grids for two-dimensional incompressible laminar and turbulent flows is presented. The necessary hierarchy of uniformly or locally refined grids is generated by a grid generation procedure especially useful for boundary layer flows. In the second part, emphasis is placed on the effect of parallelism on solvers and problems. Corresponding examples are a 2D driven cavity flow at Re=7500 and a 3D flow around a cylinder at Re=20.
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References
Bastian, P., Birken, K., Johannsen, K., Lang, S., Neuss, N., Rentz-Reichert, H., Wieners, C.: Ug - a flexible software toolbox for solving partial differential equations. Computing and Visualization in Science 1 (1997) 27–40 downloadable from ftp://ftp.ica3.uni-stuttgart.de/pub/ug/ug-3.6/ugpaper.ps.gz
Birken, K.: An efficient programming model for parallel and adaptive CFDalgorithms. Proceedings of Parallel CFD Conference 1994 (Kyoto, Japan) Elsevier Science (1995)
Hendrickson, B., Leland, R.: The Chaco User’s Guide, Version 2.0. Tech. Report 87185-110, Sandia National Laboratories, Albuquerque, New Mexico (1995) downloadable from ftp.cs.sandia.gov/pub/papers/bahendr
Huurdeman, B., Wittum, G.: Multigrid solution for 2D incompressible turbulent flows on hybrid grids. Proceedings of the ECCOMAS 98 Conference Wiley (1998)
Karimian, S.M.H., Schneider, G. E.: Pressure-based control-volume finite element method for flow at all speeds. AIAA Journal 33 (1995) No. 9 1611–1618
Meister, A.: Comparison of different Krylov subspace methods embedded in an implicit finite volume scheme for the computation of viscous and inviscid flow fields on unstructured grids. Journal of Computational Physics 140 (1998) No. 2 311–345
Menter, F. R.: Two-equation eddy-viscosity turbulence models for engineering applications. AIAA Journal 32 (1994) No. 8 1598–1605
Raw, M.J., Galpin, P.F., Hutchinson, B.R., Raithby, G.D., van Doormaal, J. P.: An element-based finite-volume method for computing viscous flows. Advanced Scientific Computing Ltd. (1994)
Schäfer, M., Turek, S.: Benchmark computations of laminar low around a cylinder. Flow Simulation with High-Performance Computers II,Notes on Numerical Fluid Mechanics Vol. 52 Vieweg Verlag (1996) 546–566
Schneider, G.E., Raw, M. J.: A skewed, positive influence coefficient upwinding procedure for control-volume-based finite element convection-diffusion computation. Numerical Heat Transfer 8 (1986) 1–26
van Doormaal, J.P., Turan, A., Raithby, G. D.: Evaluation of new techniques for the calculation of internal recirculating flows. AIAA Paper 87-0059 (1987)
van der Vorst, H. A.: Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM J. Sci. Statist. Comput. 13 (1992) 631–644
Wesseling, P.: An introduction to multigrid methods. Wiley (1991)
Wittum, G.: On the robustness of ILU smoothing. SIAM J. Sci. Stat. Comput. 10 (1989) 699–717
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Huurdeman, B., Nägele, S., Reichenberger, V., Rentz-Reichert, H. (1999). Multigrid Solution of the Incompressible Navier-Stokes Equations and its Application to Parallel Computers. In: Bungartz, HJ., Durst, F., Zenger, C. (eds) High Performance Scientific and Engineering Computing. Lecture Notes in Computational Science and Engineering, vol 8. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60155-2_5
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DOI: https://doi.org/10.1007/978-3-642-60155-2_5
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