Abstract
We describe a new algorithm for the solution of the laminar, incompressible Navier-Stokes equations for steady, two-dimensional flows. The basis of the method is a robust and efficient multigrid algorithm. A novel feature of our approach is that it dynamically adapts the grid as part of the solution process. Special interpolation operators have been used to ensure exact mass conservation. This technique can give significant savings in both CPU time and memory usage. The code has been implemented on a global shared-memory architecture, and speedups of over 13 have been observed on 20 processors. This implies that less than 2% of the code is intrinsically serial.
Keywords
- Coarse Grid
- Multigrid Algorithm
- Memory Parallel Architecture
- Computational Fluid Dynamic Problem
- Collective Relaxation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References
Bai, D., and Brandt, A. (1987) ‘Local mesh refinement multilevel techniques’, SIAM J. Sci. Stat. Comput., 8, 109–134.
Briggs, W. L. (1987) A Multigrid Tutorial, SIAM, Philadelphia.
Cliffe, K. A., Jones, I. P., Porter, J., Thompson, C. P., and Wilkes, N. S. (1983) ‘Laminar flow over a backward facing step: Solution to a test problem’, in K. Morgan, J. Periaux, F. Thomasset (eds.), Analysis of Laminar Flow over a Backward-Facing Step: A GAMM Workshop, Friedr. Vieweg and Sohn, 140–161.
Cowell, W. R., and Thompson, C. P. (1990) ‘Tools to aid in discovering parallelism and localizing arithmetic in Fortran programs’, Software Practice and Experience, 20, no. 1, 25–47.
Fearn, R. M., Mullin, T., and Cliffe, K. A. (1990) ‘Nonlinear flow phenomena in asymmetric sudden expansion’, J. Fluid Mech., 211, 595–608.
Galpin, P. F., and Raithby, A. D. (1986) ‘Numerical solution of problems in incompressible fluid flow: Treatment of temperature velocity coupling’, Num. Heat Transfer, 10, 105–129.
Gjerde, K. (1991) ‘Tools to parallelize Fortran 77 programs’, Hovedoppgave ved Institutt for Informatikk, University of Bergen.
Hackbusch, W. (1985) Multi-Grid Methods and Applications, Springer-Verlag, Berlin. 1985.
Ku, H. C, Hirsh, R. S., and Taylor, T. D. (1987) ‘A pseudospectral method for solution of the three-dimensional incompressible Navier-Stokes equations’, J. Comp. Phys., 70, 439–462.
McCormick, S., and Thomas, J. W. (1986) ‘The fast adaptive composite grid (FAC) method for elliptic equations’, Math. Comp., 46, 439–459.
Thompson, C. P. (1992) ‘The development and validation of a computational fluid dynamics code for global shared memory parallel architectures’, preprint.
Thompson, C. P., Cowell, W. R., and Leaf, G. K. (1992) ‘On the parallelization of an adaptive multigrid algorithm for a class of flow problems’, Parallel Computing, 18, 449–466.
Thompson, C. P., Leaf, G. K., and Vanka, S. P. (1988) ‘Application of a method to a buoyancy-induced flow problem’, in S. F. McCormick (ed.), Multigrid Methods, Marcel Dekker, Dordrecht, 605–629.
Thompson, C. P., Leaf, G. K., and van Rosendale, J. (1992) ‘A dynamically-adaptive multigrid algorithm for the incompressible Navier-Stokes equations — validation and model problems’, Applied Numerical Math., 9, 511–532.
Thompson, M. C., and Ferziger, J. H. (1989) ‘An adaptive multigrid technique for the incompressible Navier-Stokes equations’, J. Comp. Phys., 82, no. 1, 94–121.
Vanka, S. P. (1986) ‘Block-implicit multigrid solution of Navier-Stokes equations in primitive variables’, J. Comp. Phys., 65, no. 1, 138–158.
‘VecPar_77 tutorial introduction and reference manual’, Numerical Algorithms Group, Inc., Downers Grove, Illinois, 1990.
Winters, K. H., and Cliffe, K. A. (1979) ‘A finite element study driven laminar flow in a square cavity’, AERE - R 9444, AERE Harwell, UK.
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© 1993 Springer Science+Business Media Dordrecht
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Thompson, C.P. (1993). A Parallel Adaptive Multigrid Algorithm for the Incompressible Navier-Stokes Equations. In: Kaper, H.G., Garbey, M., Pieper, G.W. (eds) Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters. NATO ASI Series, vol 384. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1810-1_19
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DOI: https://doi.org/10.1007/978-94-011-1810-1_19
Publisher Name: Springer, Dordrecht
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