Parallel simulation of flow and transport processes

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The aim of this project is the investigation and further development of effective algorithms and software for simulation of complex flow and transport processes on parallel computers.

Fundamentals:

The treatment is based on algorithms of numerical simulation of flow and transport processes (FEM-discretization, semiimplicite time discretization of the flow problem, SUPG respectively streamline diffusion of the transport problem, hierarchically preconditioned CG's for solution of linear equation systems) and their implementation in an experimental program (2D). The domain decomposition is the fundamental parallizing idea of all parts of the simulation process. The task includes nonstationary plane, axisymmetrical and threedimensional processes, laminar and turbulent flow, coupled with transport processes of energy, species concentrations, turbulence parameters or similar quantities. The flows considered are assumed to be incompressible or variable in density at low Mach numbers.
The problems treated are typically involved with sharp boundary layers and thus the use of adaptive methods is essential. Therefore a special emphasis is focussed to the inclusion of adaptive techniques of grid generation.

Further development and implementation of the numerical algorithms in 2D and 3D.
Main topics are the attainment of a high efficiency of the parallel simulation process, an improvement of the time approximation (in particular for the flow problem) simultaneously with protection of stability of the process and investigations of applicability and robustness of adapted preconditioning techniques for the different symmetric and nonsymmetric linear systems. An important task is the development, testing and improvement of a 3D software package.
See this picture.
Development of adaptive FEM techniques on irregular hierarchical grids with the preliminary stages potential problems and 2D flow problems.
The constructed hierarchical grids with hanging nodes allow simple local refinement and coarsening and on the other hand it is possible to use multilevel methods (see project A3) for the solution of discrete systems.
See this postscript.

Applications:

laminar and turbulent inner and outer flows

thermal influenced flows and transport processes

flows with chemical reacting components, combustion processes

SPC-PMCFD2D: 2D-program system for flow and transport processes

SPC-PMCFD3D: 3D-program system for flow and transport processes

Literature:

[G1] U. Groh: Lokale Realisierung von Vektoroperationen auf Parallelrechnern.
Preprint SPC 94_2, Preprint-Reihe der Chemnitzer DFG-Forschergruppe "Scientific Parallel Computing", 1994.
[G2] U. Groh: Ein technologisches Konzept zur Erzeugung adaptiver hierarchischer Netze für FEM-Schemata.
Preprint SPC 95_6, Preprint-Reihe der Chemnitzer DFG-Forschergruppe "Scientific Parallel Computing", 1995.
[G3] U. Groh: FEM auf irregulären hierarchischen Dreiecksnetzen.
in: Proceedings, Workshop über "Paralleles wissenschaftliches Rechnen in FEM und BEM", Chemnitz, 27.09. - 30.09.1995
[G4] U. Groh: FEM auf irregulären hierarchischen Dreiecksnetzen.
Preprint SFB393/97-05, 55 S., Preprint-Reihe des SFB 393 "Numerische Simulation auf massiv parallelen Rechnern" an der Technischen Universität Chemnitz, 1997.
[G5] U. Groh, C. Israel, S. Meinel, A. Meyer: On the Numerical Simulation of Coupled Transient Problems on MIMD Parallel Systems.
Preprint SPC 94_5, Preprint-Reihe der Chemnitzer DFG-Forschergruppe "Scientific Parallel Computing", 1994.
[G6] U. Groh, S. Meinel, A. Meyer : On the Numerical Simulation of Coupled Transient Problems on MIMD Parallel Systems.
in: W. Hackbusch, G. Wittum (Hrsg.), Fast Solvers for Flow Problems, Proceedings of the Tenth GAMM-Seminar Kiel, January 14-16, 1994, Notes on Numerical Fluid Mechanics, Vol. 49, 109-120, Vieweg 1995.

[H1] G. Haase, T. Hommel, A. Meyer, M. Pester: Bibliotheken zur Entwicklung paralleler Algorithmen.
Preprint SPC 94_4, Preprint-Reihe der Chemnitzer DFG-Forschergruppe "Scientific Parallel Computing", 1994.
[H2] G. Haase, U. Langer, A. Meyer: Parallelisierung und Vorkonditionierung des CG - Verfahrens durch Gebietszerlegung.
in: G. Bader, R. Rannacher, G. Wittum (Hrsg.); Numerische Algorithmen auf Transputersystemen, Teubner-Skripten zur Numerik, Teubner-Verlag, Stuttgart 1993.

[Is1] C. Israel : Ein hierarchischer paralleler 2D-Netzgenerator für 6-Knoten-Dreiecke.
in: M.Pester (Hrsg.), Beiträge zum Workshop "Parallel Pre- und Postprocessing" der DFG-Forschergruppe "SPC", Zwickau, Juni 1993.
[Is2] C. Israel : NETGEN69 - Ein hierarchischer paralleler Netzgenerator.
Preprint SPC 95_26, Preprint-Reihe der Chemnitzer DFG-Forschergruppe "Scientific Parallel Computing", September 1995.

[Mi1] S. Meinel : Zum Konvergenzverhalten vorkonditionierter CG-Verfahren bei der Lösung von Gleichungssystemen aus der Strömungssimulation.
Workshop über "Parallele Lösung großer Gleichungssysteme", Chemnitz, 27.-28.05.1994.
[Mi2] S. Meinel : Probleme der Simulation komplexer Strömungsvorgänge unter Einbeziehung von Parallelrechnern.
Jahrestagung der DMV 1996, Jena, 15.-23.09.1996.
[Mi3] S. Meinel, A. Meyer: A parallel algorithm for simulation of incompressible transient flows.
in: Bader, G., Rannacher R., Wittum G. (Hrsg.), Beiträge zum Workshop "Parallel Solution Methods for Differential Equations", 6.-7. Nov. 1992 an der Universität Heidelberg.
[Mi4] S. Meinel, A. Meyer: Grundlagen eines Strömungssimulationsprogramms für MIMD-Parallelrechner.
Unveröff. Forschungsbericht, TU Chemnitz-Zwickau, 1993.

[My1] A. Meyer: A parallel preconditioned conjugate gradient method using domain decomposition and inexact solvers on each subdomain.
Computing, 45:217-234, 1990.
[My2] A. Meyer: The Concept of Special Inner Products for Deriving New Conjugate Gradient-like Solvers for Non-symmetric Sparse Linear Systems.
Num. Lin. Alg. Appl. 1(2), 129-139, 1994
[My3] A. Meyer: Preconditioning the Pseudo-Laplacian for Finite Element Simulation of Incompressible Flow.
Preprint SPC 94_19, Preprint-Reihe der Chemnitzer DFG-Forschergruppe "Scientific Parallel Computing", 1994.
[My4] A. Meyer, S. Meinel, U. Groh: Parallel finite element simulation of coupled flow problems.
in: Knop, Schreiber (Eds.); Power Explorer User Report, Second Edition, 144-150, Düsseldorf 1995.
[My5] A. Meyer, M. Pester: Verarbeitung von Sparse-Matrizen in Kompaktspeicherform (KLZ / KZU).
Preprint SPC 94_12, Preprint-Reihe der Chemnitzer DFG-Forschergruppe "Scientific Parallel Computing", 1994.
[My6] A. Meyer, S. Meinel, C. Israel, K.-J. Kohl, R. Grabski: Numerical Simulation of Fire Spread on a MIMD Parallel Computer.
Fifth Int. Conf. on Numerical Combustion, Garmisch-Partenkirchen, 29.9.-1.10.1993.

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H. Rhein, October 1997

S. Meinel, C. Israel, February 1998