A parallelization technique applied to the computation of rotating flows in cavities
Resumo
In this paper, we investigate the parallel solution to the rotating internal flow problems, using the Navier-Stokes equations as proposed in [ST83] and [SPE85]. A Runge-Kutta time-stepping scheme was applied to the equations and both sequential and message-passing implementations were developed, the latter using MPI, and were tested on an SGI Origin200 distributed, global shared memory parallel computer. The results show that our approach to parallelize the sequential implementation requires little effort whilst providing good results even for medium-sized problems, on this particular computer.
Palavras-chave:
Parallel computing, Message-passing, Computational Fluid Dynamics
Referências
R.D. da Cunha. A benchmark study based on the parallel computation of the vector outer-product α = uvT operation. Concurrency: Practice & Experience, 9(8):803-819, August 1997.
A.L. de Bortoli. Solution of incompressible flows using a compressible flow solver. 129-94/18, DLR-IB, 1994.
R.D. da Cunha and T.R. Hopkins. Parallel preconditioned Conjugate-Gradients methods on transputer networks. Transputer Communications, 1(2):111-125, 1993. Also as TR-5-93, Computing Laboratory, University of Kent at Canterbury, U.K.
R.D. da Cunha and T.R. Hopkins. A parallel implementation of the restaned GMRES iterative method for nonsymmetric systems of linear equations. Advances in Computational Mathematics, 2(3):261-277, April 1994. Also as TR-7-93, Computing Laboratory, University of Kent at Canterbury.
R.D. da Cunha and T.R. Hopkins. The Parallel Iterative Methods (PIM) package for the solution of systems of linear equations on parallel computers. Applied Numerical Muthematics, 19(1-2):33-50, November 1995.
E. Dick. Introduction to Finite Volume Techniques in Computational Fluid Dynamics, pages 270-297. J.F. Wendt (Ed.), Computational Fluid Dynamics - An Introduction (2nd Ed.). Springer-Verlag, Berlin, 1996.
C.A.J. Fletcher. Computational Techniques for Fluid Dynamics. Spring-Verlag, Berlin, 2nd edition, 1991.
Message Passing Interface Forum. MPI: A message-passing interface standard. TR CS-93-214, University of Tennessee, November 1993.
J.H. Ferziger and M. Peric. Compututional Methods for Fluid Dynamics. Springer-Verlag, Berlin, 1996.
A. Jameson, W. Schmidt, and E. Turkel. Numerical solution of the Euler equations by finite volume methods using Runge-Kutta time-stepping schemes. AIAA Paper 81-1259. 1981.
D.A.R. Justo. Visual. Manual do usuário, Laboratório Integrado de Computação Científica. Instituto de Matemática. Universidade Federal do Rio Grande do Sul, 1998.
V. Kalro and T. Tezduyar. Parallel 3D computation of unsteady tlows around circular cylinders. Parallel Computing, 23:1235- 1248, 1997.
L. Paglieri, D. Ambrosi, L. Formaggia, A. Quaneroni, and A.L. Scheinine. Parallel computation for shallow water flow: a domain decomposition approach. Parallel Computing. 23:1261- 1277. 1997.
N. Satofuka, M. Obata, and T. Suzuki. Parallel computation of super-/hypersonic flows on workstation network and Transputer arrays. Parallel Computing, 23: 1293-1305, 1997.
C.G. Speziale. Numerical solution of rotating internal flows. Lectures in Applied Mathematics, 22:261-288, 1985.
C.G. Speziale and S. Thangam. Numerical study of secondary flows and roll-cell instabilities in rotating channel flow. Journal of Fluid Mechanics, 130:377-395, 1983.
A.L. de Bortoli. Solution of incompressible flows using a compressible flow solver. 129-94/18, DLR-IB, 1994.
R.D. da Cunha and T.R. Hopkins. Parallel preconditioned Conjugate-Gradients methods on transputer networks. Transputer Communications, 1(2):111-125, 1993. Also as TR-5-93, Computing Laboratory, University of Kent at Canterbury, U.K.
R.D. da Cunha and T.R. Hopkins. A parallel implementation of the restaned GMRES iterative method for nonsymmetric systems of linear equations. Advances in Computational Mathematics, 2(3):261-277, April 1994. Also as TR-7-93, Computing Laboratory, University of Kent at Canterbury.
R.D. da Cunha and T.R. Hopkins. The Parallel Iterative Methods (PIM) package for the solution of systems of linear equations on parallel computers. Applied Numerical Muthematics, 19(1-2):33-50, November 1995.
E. Dick. Introduction to Finite Volume Techniques in Computational Fluid Dynamics, pages 270-297. J.F. Wendt (Ed.), Computational Fluid Dynamics - An Introduction (2nd Ed.). Springer-Verlag, Berlin, 1996.
C.A.J. Fletcher. Computational Techniques for Fluid Dynamics. Spring-Verlag, Berlin, 2nd edition, 1991.
Message Passing Interface Forum. MPI: A message-passing interface standard. TR CS-93-214, University of Tennessee, November 1993.
J.H. Ferziger and M. Peric. Compututional Methods for Fluid Dynamics. Springer-Verlag, Berlin, 1996.
A. Jameson, W. Schmidt, and E. Turkel. Numerical solution of the Euler equations by finite volume methods using Runge-Kutta time-stepping schemes. AIAA Paper 81-1259. 1981.
D.A.R. Justo. Visual. Manual do usuário, Laboratório Integrado de Computação Científica. Instituto de Matemática. Universidade Federal do Rio Grande do Sul, 1998.
V. Kalro and T. Tezduyar. Parallel 3D computation of unsteady tlows around circular cylinders. Parallel Computing, 23:1235- 1248, 1997.
L. Paglieri, D. Ambrosi, L. Formaggia, A. Quaneroni, and A.L. Scheinine. Parallel computation for shallow water flow: a domain decomposition approach. Parallel Computing. 23:1261- 1277. 1997.
N. Satofuka, M. Obata, and T. Suzuki. Parallel computation of super-/hypersonic flows on workstation network and Transputer arrays. Parallel Computing, 23: 1293-1305, 1997.
C.G. Speziale. Numerical solution of rotating internal flows. Lectures in Applied Mathematics, 22:261-288, 1985.
C.G. Speziale and S. Thangam. Numerical study of secondary flows and roll-cell instabilities in rotating channel flow. Journal of Fluid Mechanics, 130:377-395, 1983.
Publicado
29/09/1999
Como Citar
CUNHA, Rudnei Dias da; BORTOLI, Álvaro Luiz de.
A parallelization technique applied to the computation of rotating flows in cavities. In: INTERNATIONAL SYMPOSIUM ON COMPUTER ARCHITECTURE AND HIGH PERFORMANCE COMPUTING (SBAC-PAD), 11. , 1999, Natal.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
1999
.
p. 77-84.
DOI: https://doi.org/10.5753/sbac-pad.1999.19774.
