Abstract
This paper describes the numerical method of solution of 3D Navier-Stokes equations in a regular domain and direct method of parallelization of solution for distributed-memory computers. A vorticityvector -potential formulation and Finite Difference method of solution are chosen, using fractional step ADI method for vorticity equation and Fourier method for Poisson equation. Special attention is paid to singleprocessor optimization of the algorithm. Parallelization technology is given in detail, with speedup and efficiency levels achieved for 2 and 4 processors. Numerical results are presented for different geometries and Reynolds numbers.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
J.R. Koseff, R.L. Street. The lid-driven cavity flow: A synthesis of qualitative and quantitative observations. J. Fluids Engin., 106, 390–398, 1984.
Numerical Simulation of 3-D Incompressible Unsteady Viscous Laminar Flows: A GAMM Workshop/ed. by M. Deville et al. Notes on Numerical Fluid Mechanics, 36, Vieweg, 1992.
V.A. Romanov. Stability of plane parallel Couette flow. Doklady Akademii Nauk SSSR, 196, No. 5, 1971.
B.L. Rozhdestvensky, I.I. Simakin, M.I. Stoinov. Simulation of turbulent Couette flow in a flat channel. Preprint of the Institute of Applied Mathematics, Academy of Sciences of USSR, 106, 1987.
H.W. Ryu, D.I. Lee. Numerical study of viscous flow in rectangular cavities with translating top and bottom walls. Proceedings of the Third Pacific Chemical Engineering Congress, Seoul, Korea, 1983.
S.A. Baranov, V.A. Brailovskaya, V.R. Kogan, L.V. Feoktistova. Numerical investigation of fluid flows in a plane and volume cavity. Proceedings of X Congress in Mechanics, Paris, 1991.
G. Guj, F. Stella. A vorticity-velocity method for the numerical solution of 3D incompressible flows. J. Comput. Phys., 106, 286–298, 1993.
P.J. Roache. Computational Fluid Dynamics. Albuquerque, Hermosa Publishers, 1976.
C.J. Freitas, R.L. Street, A.N. Findikakis, J.R. Koseff. Numerical simulation of three-dimensional flow in a cavity. Int. J. Num. Meth. Fl., 5, 561–575, 1985.
C.Y. Perng, R.L. Street. Three-dimensional unsteady flow simulations: Alternative strategies for a volume-averaged calculations. Int. J. Num. Meth. Fl., 9, 341–362, 1989.
R.W. Hockney. A fast direct solution of Poisson's equation using Fourier analysis. J. Assoc. Comput. Math., 12, 95–113, 1965.
J.M. Ortega. Introduction to Parallel and Vector Solution of Linear Systems. Plenum Press, 1988.
L. Johnsson. Solving narrow banded systems on ensemble architectures. ACM Trans. Math. Software, 11, 1985.
C. Walshaw, S.J. Farr. A two-way parallel partition method for solving tridiagonal systems. University of Leeds, U.K., School of Computer Studies Research Report Series, Report 93.25, 1993.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bessonov, O., Brailovskaya, V., Polezhaev, V., Roux, B. (1995). Parallelization of the solution of 3D Navier-Stokes equations for fluid flow in a cavity with moving covers. In: Malyshkin, V. (eds) Parallel Computing Technologies. PaCT 1995. Lecture Notes in Computer Science, vol 964. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60222-4_127
Download citation
DOI: https://doi.org/10.1007/3-540-60222-4_127
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60222-4
Online ISBN: 978-3-540-44754-2
eBook Packages: Springer Book Archive