Table of Content

Open Access iconOpen Access

ARTICLE

On the Efficiency of the Parallel-in-Time Finite Volume Calculation of the Unsteady Navier-Stokes Equations

J. M. F. Trindade1, J. C. F. Pereira2

Escola Náutica Infante D. Henrique, Av. Bonneville Franco, 2780-572 Pa co d’Arcos, Portugal.(jor-getrindade@enautica.pt)
Instituto Superior Técnico, Universidade Técnica de Lis-boa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal. (jcf-pereira@mail.ist.utl.pt)

Computer Modeling in Engineering & Sciences 2007, 20(1), 1-10. https://doi.org/10.3970/cmes.2007.020.001

Abstract

In this paper, we discuss the efficiency and speed-up of parallel-in-time calculations of the unsteady incompressible Navier-Stokes equations in a PC-cluster. The parallel-in-time method is based on the alternate use of coarse global sequential solvers with fine local parallel ones in an iterative predictor-corrector fashion. Therefore, the efficiency of parallel calculations is strongly dependent on the number of iterations required for convergence. The one-dimensional scalar transport equation and the two-dimensional incompressible unsteady form of the Navier-Stokes equations were used to conduct numerical experiments to derive some conclusions concerning the accuracy and convergence of the iterative method. A simple performance model is proposed to estimate the efficiency of the parallel calculations as a function of the most relevant parameters that contribute to the computing time required to perform a parallel-in-time calculation. Among them, we have analyzed the influence of the number of processors, the number of iterations in the parallel-in-time algorithm and the influence of the coarse to fine time-grid step size ratio. The good agreement between the obtained parallel efficiency and the values estimated by the proposed performance model allows to conclude that parallel-in-time efficiency is quantitatively different from the parallel efficiency of the space domain decomposition, regarding the number of processors available for a fixed problem dimension. A significant speed-up is possible when the temporal scale of the problem is large and enough processors are available.

Keywords


Cite This Article

APA Style
Trindade, J.M.F., Pereira, J.C.F. (2007). On the efficiency of the parallel-in-time finite volume calculation of the unsteady navier-stokes equations. Computer Modeling in Engineering & Sciences, 20(1), 1-10. https://doi.org/10.3970/cmes.2007.020.001
Vancouver Style
Trindade JMF, Pereira JCF. On the efficiency of the parallel-in-time finite volume calculation of the unsteady navier-stokes equations. Comput Model Eng Sci. 2007;20(1):1-10 https://doi.org/10.3970/cmes.2007.020.001
IEEE Style
J.M.F. Trindade and J.C.F. Pereira, "On the Efficiency of the Parallel-in-Time Finite Volume Calculation of the Unsteady Navier-Stokes Equations," Comput. Model. Eng. Sci., vol. 20, no. 1, pp. 1-10. 2007. https://doi.org/10.3970/cmes.2007.020.001



cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
  • 1344

    View

  • 1158

    Download

  • 0

    Like

Share Link