Parallelization of the compact methods for the Navier-Stokes equations

  • Jacek Rokicki Warsaw University of Technology
  • Jerzy M. Floryan The University of Western Ontario

Abstract

The proposed algorithm is based on the fourth-order compact discretization schemes for the Navier-Stokes equations in streamfunction-vorticity-pressure formulation. The equations are expressed in terms of a general orthogonal curvilinear coordinate system which allows for modelling non-standard geometries. Two distinct parallelization strategies are considered. The first one relies on the domain decomposition approach, in which each sub domain is served by a different processor. In the second strategy, suitable for massively parallel computers, each processor serves a single grid point . The comparison of the performance of various computing platforms is presented, including a 2048-processor MasPar computer.

Keywords

References

[1] S.C.R. Dennis, J.D. Hudson. A difference method for solving the Navier-Stokes equations. In: C. Taylor et al., eds., Proceedings of the First International Conference on Numerical Methods in Laminar and Turbulent Flow, 69- 80, Pentech Press, London, 1978.
[2] S.C.R. Dennis, J.D. Hudson. Compact h4 finite-difference approximations to operators of Navier-Stokes type. J. Comput. Phys., 85: 390-416, 1989.
[3] M.M. Gupta, R.P. Manohar. Boundary approximations and accuracy in viscous flow computations. J. Comput. Phys., 31: 265-288, 1979.
[4] J. Rokicki, J .M. Floryan. Multiprocessor implementation of the compact finite-difference method for the Navier-Stokes equations. Expert Systems in Fluid Dynamics Research Laboratory, Report ESFD - 3/93, Department of Mechanical Engineering, The University of Western Ontario, London, Ontario, Canada, 1993.
[5] J. Rokicki, J .M. Floryan. Compact fourth-order algorithm for the Navier-Stokes equations in terms of general orthogonal coordinate system. Expert Systems in Fluid Dynamics Research Laboratory, Report ESFD - 5/93, Department of Mechanical Engineering, The University of Western Ontario, London, Ontario, Canada, 1993.
Published
Aug 31, 2023
How to Cite
ROKICKI, Jacek; FLORYAN, Jerzy M.. Parallelization of the compact methods for the Navier-Stokes equations. Computer Assisted Methods in Engineering and Science, [S.l.], v. 1, n. 3-4, p. 147-157, aug. 2023. ISSN 2956-5839. Available at: <https://cames.ippt.gov.pl/index.php/cames/article/view/1518>. Date accessed: 13 nov. 2024.
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Issue
Vol 1 No 3-4 (1994)
Section
Articles
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