Parallel simulation of flow and transport processes

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	Members
	Motivation
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Aim:

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

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Members:

• Prof. Dr. Arnd Meyer
• Dr. Stefan Meinel

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  Motivation:

  The treatment is based on algorithms for numerical flow simulation (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 in all pieces of the simulation process. The task includes instationary plane, axi-symmetric and threedimensional processes, laminar and turbulent flows, coupled with transport processes of energy, substance concentrations, turbulence parameters or similar quantities. The contemplated flows are uncompressible or variable in density at low Mach numbers. We treat problems for which the formation of sharp boundary layers is typical and in that reason require the utilization of adaptiv methods. Therefore, the integration of adaptiv techniques of grid generation is an emphasis of this project.

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  Projects:

  • Further development and implementation of the fundamental numerical process in the task mentioned above. Especially it concerns the realization of a high efficiency of the parallel simulation process, the improvement of the time approximation (particularly in the flow problem) with simoultaneously protection of stability of the process and investigations of use and robustness of adapted preconditioning techniques for the different symmetric and nonsymmetric linear partial systems. An emphasis is the elaboration, the testing and the expansion of a 3D software package.
    See this picture.
  • Development of adaptive FEM techniques on irregular hierarchical grid with the partial steps potential problems and 2D flow problems
    Hierarchical grids with hanging nodes allow simple local refinement and coarsening and utilization of multilevel processes (see project A3 on solution of discrete systems).
    See this postscript.

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  Applications:

  • laminar and turbulent inside and outside flow processes
  • thermal influenced flows, transport processes
  • flows with chemical reacting components, combustion processes

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  Software:

  • SPC-PMCFD2D: 2D-program system for flow and transport processes
  • SPC-PMCFD3D: 3D-program system for flow and transport processes

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  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.
  [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 Stroemungsvorgänge 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.), Beitr\äge zum Workshop "Parallel Solution Methods for Differential Equations", 6.-7. Nov. 1992 an der Universit\ät Heidelberg.
  [Mi4] S. Meinel, A. Meyer: Grundlagen eines Strömungssimulationsprogramms für MIMD-Parallel\-rechner.
  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