Abstract
Two programs for the simulation of viscous flows were implemented on Parsytec Transputer and Intel i860 systems.
The first case is an explicit solution scheme with possible multigrid acceleration for the computation of three dimensional steady or unsteady flows. Parallelization of this algorithm is straightforward. Efficiency values for different processor numbers are presented and discussed. Overall computing times are compared to those of different super vector computers.
The second algorithm is an implicit scheme for unsteady incompressible flows based on the artificial compressibility approach. The linear system of equations arising in this problem is solved with a Gauß-Seidel line relaxation technique. This involves the inversion of a big number of block-tridiagonal equations. Six different methods for their solution were applied and compared with each other.
Part of this material is based upon work supported by the NSF under Cooperative Agreement No. CCR-8809615. Access to the Intel Touchstone Delta was provided by the Concurrent SuperComputing Consortium.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Si Bondeli. Divide and conquer: a parallel algorithm for the solution of a tridiagonal system of equations. Parallel Computing, 17: 419–434, 1991.
M. Breuer. Numerische Lösung der Navier-Stokes Gleichungen für dreidimensio-nale inkompressible instationäre Strömungen zur Simulation des Wirbelaufplatzens. Dissertation, Aerodynamisches Institut, RWTH Aachen, 1991.
M. Breuer and D. Hänel. A Dual Time-Stepping Method for 3-D, Viscous, Incom-pressible Vortex Flows. Computers and Fluids, 1993.
A.J. Chorin. A Numerical Method for Solving Incompressible Viscous Flow. J. Comput. Phys., 2: 12–26, 196T.
A. Frommer. Lösung linearer Gleichungssysteme auf Parallelrechnern. Vieweg Verlag, Braunschweig, 1990.
A. Harten. On a Class of High Resolution Total-Variation-Stable Finite- Difference Schemes for Hyperbolic Conservation Laws. SI AM J. Numer, Anal 21, 1984.
R.W. Hockney. A Fast and Direct Solution of Poisson’s Equation Using Fourier Analysis. J. ACM, 1 (12): 95–113, 1965.
M. Meinke and D. Hänel. Simulation of unsteady flows. In K. W. Morton, editor, 12th International Conference on Numerical Methods in Fluid Dynamics, pages 268–272. Springer Verlag, July 1990.
M. Meinke and E. Ortner. Implementation of explicit navier-stokes solvers on massively parallel systems. In E. H. Hirschel, editor, Notes on Numerical Fluid Mechanics, volume 38, pages 138–151. Vieweg Verlag, 1993.
P.L. Roe. Approximate Riemann Solvers, Parameter Vectors and Difference Schemes. J. Comp. Phys., 22: 357, 1981.
H.H. Wang. A Parallel Method for Tridiagonai Equations. ACM Trans. Math. Software, 7 (2): 170–183, 1981.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Meinke, M., Hofhaus, J. (1993). Parallel Solution Schemes for the Navier-Stokes Equations. In: Meuer, HW. (eds) Supercomputer ’93. Informatik aktuell. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-78348-7_14
Download citation
DOI: https://doi.org/10.1007/978-3-642-78348-7_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-56948-0
Online ISBN: 978-3-642-78348-7
eBook Packages: Springer Book Archive