Summary
PASTIS-3D (Projection Algorithm Solver for Time-dependent Incompressible flow Simulations in 3 Dimensions) is a computer program for the solution of the incompressible time-dependent Navier-Stokes equations. It uses the implicit projection-2 algorithm [9], which is 2nd order accurate [16] for the velocities. It works with a data parallel variant of the conjugate gradient method [13], [10] to run efficiently on parallel systems such as workstation clusters and the IBM Scalable POWERparallel Systems (9076 SPx). The parallel data structure is familiar from domain decomposition. But, we use a parallel implementation of a sequential algorithm and hence obtain the desired sequential results.
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
Bell, J.B. and D.L. Marcus, A Second-Order Projection Method For Variable-Density Flows, UCRL-JC-104123, LLNL, Livermore, CA, 1990.
Bergen, O., Numerische Simulation der Strömung und des Transports wasserlöslicher Stoffe in Seen und Talsperren am Beispiel des Vorbeckens der Möhnetalsperre, Thesis, Inst. f. Wasserbau, RWTH Aachen, 1993.
Chorin, A.J., Numerical Solution of the Navier-Stokes Equations, Math. Comp., 22, 1968, 745–763.
Daniels, H., PASTIS-3D Finite Element Projection Algorithm Solver for Transient Incompressible Flow Simulations - Manual, UCRL-MA-111833, LLNL, Livermore, CA, 1992.
Daniels, H. and A. Peters, Solving Large Incompressible Time-Dependent Flow Problems on Scalable Parallel Systems, prep. for Int. J. Num. Meth. Fluids, IBM TR 75.94, 1994.
Dryja, M., A finite element capacitance method for elliptic problems on regions partitioned into subdomains, Numer. Math., 44, 1984, 153–168.
Geist, A., A. Beguelin, J. Dongarra, W. Jiang, R. Manchek and V. Sunderam, PVM 3 User’s Guide and Manual, Report No. ORNL/TM-12187, Eng. Phys. and Math. Div., ORNL, Oak Ridge, TN, 1993.
Emmons H.W., Annu. Rev. Fluid Mech., 2, 15, 1970.
Gresho, P.M., On the theory of semi-implicit projection methods for viscous incompressible flow and its implementation via a finite element method that also introduces a nearly-consistent mass matrix, Part 1: Theory, Int. J. Num. Meth. Fluids, 11, 1990, 587–620.
Haase, G. and U. Langer, Parallelisierung und Vorkonditionierung des CG-Verfahrens durch Gebietszerlegung, Num. Algebra auf Transputersystemen, Teubner, May 1993.
Harlow, F.H. and J.E. Welch, Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluids with Free Surface, Physics of Fluids, 8, No. 12, 1965, 2182–2189.
Karniadakis G.E. and S.A. Orszag, Nodes, Modes, and Flow Codes, Physics Today, 46, No. 3, 1993, 34–42.
Keyes, D.E. and W.D. Gropp, A comparison of domain decompositions techniques for elliptic partial differential equations and their parallel implementation, SIAM J. SCI. STAT. COMPUT., 8, No. 2, 1987, 166–202.
Peters, A., Non-symmetric CG-like schemes and the finite element solution of the advection-dispersion equation, Int. J. Num. Meth. Fluids, 17, 1993, 955–974.
Schmidt, P., Vorkonditioniertes paralleles Verfahren der konjugierten Gradienten für elliptische Differentialgleichungen, Thesis, Prakt. Math., Karlsruhe Univ., IBM, 1993.
Shin, J., On Error Estimates of Some Higher Order Projection and Penalty-Projection Methods for Navier-Stokes Equations, Report No. A1190, Dept. of Math., Penn State, subm. Num. Mathematik, 1991.
Témam, R., Sur l’approximation de la solution des équation de Navier-Stokes par la méthode des pas fractionnaires (I), Arch. R.t. Mech. Anal., 32, 1969, 135–153.
Van Kan, J., A Second-Order Accurate Pressure Correction Scheme for Viscous Incompressible Flow, SIAM J. Sci. Comp., 7, No. 3, 1986, 870–891.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1994 Springer Fachmedien Wiesbaden
About this chapter
Cite this chapter
Daniels, H., Peters, A. (1994). PASTIS-3D — A Parallel Finite Element Projection Code for the Time- Dependent Incompressible Navier-Stokes Equations. In: Hebeker, FK., Rannacher, R., Wittum, G. (eds) Numerical methods for the Navier-Stokes equations. Notes on Numerical Fluid Mechanics (NNFM), vol 47. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-14007-8_4
Download citation
DOI: https://doi.org/10.1007/978-3-663-14007-8_4
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-528-07647-4
Online ISBN: 978-3-663-14007-8
eBook Packages: Springer Book Archive