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2020 | OriginalPaper | Chapter

12. Steigerung der Effizienz und der Genauigkeit

Authors : Joel H. Ferziger, Milovan Perić, Robert L. Street

Published in: Numerische Strömungsmechanik

Publisher: Springer Berlin Heidelberg

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Zusammenfassung

Dieses Kapitel ist der Genauigkeits- und Effizienzsteigerung und der Qualität numerischer Gitter für komplexe Geometrien gewidmet. Zuerst wird die Effizienzsteigerung durch Mehrgitteralgorithmen beschrieben, gefolgt von Beispielen. Adaptive Gittermethoden und lokale Gitterverfeinerung sind Gegenstand eines weiteren Abschnitts. Schließlich wird die Parallelisierung diskutiert. Besondere Aufmerksamkeit wird der Parallelverarbeitung für implizite Methoden, die auf der Gebietszerlegung in Raum und Zeit basieren, und der Analyse der Effizienz der Parallelverarbeitung gewidmet. Zur Veranschaulichung dieser Punkte werden Beispielberechnungen verwendet.

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Literature
go back to reference Adams, M., Colell, P., Graves, D. T., Johnson, J. N., Johansen, H. S., Keen, N. D., ... Van Straalen, B. (2015). Chombo software package for AMR application design document (Bericht). Lawrence Berkeley National Laboratory, Berkeley, CA: Applied Numerical Algorithms Group, Computational Research Division. Adams, M., Colell, P., Graves, D. T., Johnson, J. N., Johansen, H. S., Keen, N. D., ... Van Straalen, B. (2015). Chombo software package for AMR application design document (Bericht). Lawrence Berkeley National Laboratory, Berkeley, CA: Applied Numerical Algorithms Group, Computational Research Division.
go back to reference Bastian, P. & Horton, G. (1989). Parallelization of robust multi-grid methods: ILU factorization and frequency decomposition method. In W. Hackbusch & R. Rannacher (Hrsg.), Notes on numerical fluid mechanics (Bd. 30, S. 24–36). Braunschweig: Vieweg. Bastian, P. & Horton, G. (1989). Parallelization of robust multi-grid methods: ILU factorization and frequency decomposition method. In W. Hackbusch & R. Rannacher (Hrsg.), Notes on numerical fluid mechanics (Bd. 30, S. 24–36). Braunschweig: Vieweg.
go back to reference Berger, M. J. & Oliger, J. (1984). Adaptive mesh refinement for hyperbolic partial differential equations. J. Comput. Phys., 53, 484–512. Berger, M. J. & Oliger, J. (1984). Adaptive mesh refinement for hyperbolic partial differential equations. J. Comput. Phys., 53, 484–512.
go back to reference Bijl, H., Lucor, D., Mishra, S. & Schwab, C. (2013). Uncertainty quantification in computational fluid dynamics. Switzerland: Springer International Publishing. Bijl, H., Lucor, D., Mishra, S. & Schwab, C. (2013). Uncertainty quantification in computational fluid dynamics. Switzerland: Springer International Publishing.
go back to reference Bradshaw, P., Launder, B. E. & J. L. Lumley, J. L. (1994). Collaborative testing of turbulence models. In K. N. Ghia, U. Ghia & D. Goldstein (Hrsg.), Advances in computational fluid mechanics (Bd. 196), New York: ASME. Bradshaw, P., Launder, B. E. & J. L. Lumley, J. L. (1994). Collaborative testing of turbulence models. In K. N. Ghia, U. Ghia & D. Goldstein (Hrsg.), Advances in computational fluid mechanics (Bd. 196), New York: ASME.
go back to reference Briggs, W. L., Henson, V. E. & McCormick, S. F. (2000). A multigrid tutorial (2. Aufl.). Philadelphia: Society for Industrial and Applied Mathematics (SIAM). Briggs, W. L., Henson, V. E. & McCormick, S. F. (2000). A multigrid tutorial (2. Aufl.). Philadelphia: Society for Industrial and Applied Mathematics (SIAM).
go back to reference Bryan, G. H., Wyngaard, J. C. & Fritsch, J. M. (2003). Resolution requirements for the simulation of deep moist convection. Mon. Weather Rev., 131, 2394–2416. Bryan, G. H., Wyngaard, J. C. & Fritsch, J. M. (2003). Resolution requirements for the simulation of deep moist convection. Mon. Weather Rev., 131, 2394–2416.
go back to reference Burmeister, J. & Horton, G. (1991). Time-parallel solution of the Navier-Stokes equations. In Proc. 3rd European Multigrid Conference. Basel: Birkhäuser Verlag. Burmeister, J. & Horton, G. (1991). Time-parallel solution of the Navier-Stokes equations. In Proc. 3rd European Multigrid Conference. Basel: Birkhäuser Verlag.
go back to reference Caruso, S. C., Ferziger, J. H. & Oliger, J. (1985). An adaptive grid method for incompressible flows (Bericht Nr. TF-23). Stanford CA: Dept. Mech. Engrg., Stanford University. Caruso, S. C., Ferziger, J. H. & Oliger, J. (1985). An adaptive grid method for incompressible flows (Bericht Nr. TF-23). Stanford CA: Dept. Mech. Engrg., Stanford University.
go back to reference Celik, I., Ghia, U., Roache, P. J. & Freitas, C. J. (2008). Procedure for estimation and reporting of uncertainty due to discretization in cfd applications. J. Fluids Engrg., 130, 078001. Celik, I., Ghia, U., Roache, P. J. & Freitas, C. J. (2008). Procedure for estimation and reporting of uncertainty due to discretization in cfd applications. J. Fluids Engrg., 130, 078001.
go back to reference Demmel, J. W., Heath, M. T. & van der Vorst, H. A. (1993). Parallel numerical linear algebra. Acta Numerica, 2, 111–197. Demmel, J. W., Heath, M. T. & van der Vorst, H. A. (1993). Parallel numerical linear algebra. Acta Numerica, 2, 111–197.
go back to reference Ferziger, J. H. & Perić, M. (1996). Further discussion of numerical errors in CFD. Int. J. Numer. Methods Fluids, 23, 1–12. Ferziger, J. H. & Perić, M. (1996). Further discussion of numerical errors in CFD. Int. J. Numer. Methods Fluids, 23, 1–12.
go back to reference Hackbusch, W. & Trottenberg, U. (Hrsg.). (1991). Proc. Third European Multigrid Conference, International Series of Numerical Mathematics. Basel: Birkhäuser Verlag. Hackbusch, W. & Trottenberg, U. (Hrsg.). (1991). Proc. Third European Multigrid Conference, International Series of Numerical Mathematics. Basel: Birkhäuser Verlag.
go back to reference Hackbusch, W. (1984). Parabolic multi-grid methods. In R. Glowinski & J.-R. Lions (Hrsg.), Computing methods in applied sciences and engineering. Amsterdam: North Holland. Hackbusch, W. (1984). Parabolic multi-grid methods. In R. Glowinski & J.-R. Lions (Hrsg.), Computing methods in applied sciences and engineering. Amsterdam: North Holland.
go back to reference Hackbusch, W. (2003). Multi-grid methods and applications (2nd Printing). Berlin: Springer. Hackbusch, W. (2003). Multi-grid methods and applications (2nd Printing). Berlin: Springer.
go back to reference Harrison, R. J. (1991). Portable tools and applications for parallel computers. Int. J. Quantum Chem., 40, 847–863. Harrison, R. J. (1991). Portable tools and applications for parallel computers. Int. J. Quantum Chem., 40, 847–863.
go back to reference Hortmann, M., Perić, M. & Scheuerer, G. (1990). Finite volume multigrid prediction of laminar natural convection: bench-mark solutions. Int. J. Numer. Methods Fluids, 11, 189–207. Hortmann, M., Perić, M. & Scheuerer, G. (1990). Finite volume multigrid prediction of laminar natural convection: bench-mark solutions. Int. J. Numer. Methods Fluids, 11, 189–207.
go back to reference Horton, G. (1991). Ein zeitparalleles Lösungsverfahren für die Navier-Stokes-Gleichungen PhD Dissertation. Universität Erlangen-Nürnberg. Horton, G. (1991). Ein zeitparalleles Lösungsverfahren für die Navier-Stokes-Gleichungen PhD Dissertation. Universität Erlangen-Nürnberg.
go back to reference Hutchinson, B. R. & Raithby, G. D. (1986). A multigrid method based on the additive correction strategy. Numer. Heat Transfer, 9, 511–537. Hutchinson, B. R. & Raithby, G. D. (1986). A multigrid method based on the additive correction strategy. Numer. Heat Transfer, 9, 511–537.
go back to reference Hutchinson, B. R., Galpin, P. F. & Raithby, G. D. (1988). Application of additive correction multigrid to the coupled fluid flow equations. Numer. Heat Transfer, 13, 133–147. Hutchinson, B. R., Galpin, P. F. & Raithby, G. D. (1988). Application of additive correction multigrid to the coupled fluid flow equations. Numer. Heat Transfer, 13, 133–147.
go back to reference Khajeh-Saeed, A. & Perot, J. B. (2013). Direct numerical simulation of turbulence using GPU accelerated supercomputers. J. Comput. Phys., 235, 241–257. Khajeh-Saeed, A. & Perot, J. B. (2013). Direct numerical simulation of turbulence using GPU accelerated supercomputers. J. Comput. Phys., 235, 241–257.
go back to reference Lilek, Ž. (1995). Ein Finite-Volumen Verfahren zur Berechnung von inkompressiblen und kompressiblen Strömungen in komplexen Geometrien mit beweglichen Rndern und freien Oberflächen (PhD Dissertation). University of Hamburg, Germany. Lilek, Ž. (1995). Ein Finite-Volumen Verfahren zur Berechnung von inkompressiblen und kompressiblen Strömungen in komplexen Geometrien mit beweglichen Rndern und freien Oberflächen (PhD Dissertation). University of Hamburg, Germany.
go back to reference Lilek, Ž., Muzaferija, S. & Perić, M. (1997a). Efficiency and accuracy aspects of a full-multigrid SIMPLE algorithm for three-dimensional flows. Numer. Heat Transfer, Part B, 31, 23–42. Lilek, Ž., Muzaferija, S. & Perić, M. (1997a). Efficiency and accuracy aspects of a full-multigrid SIMPLE algorithm for three-dimensional flows. Numer. Heat Transfer, Part B, 31, 23–42.
go back to reference Lilek, Ž., Nadarajah, S., Perić, M., Tindal, M. & Yianneskis, M. (1991). Measurement and simulation of the flow around a poppet valve. In Proc. 8th symp. turbulent shear flows (S. 13.2.1–13.2.6). Lilek, Ž., Nadarajah, S., Perić, M., Tindal, M. & Yianneskis, M. (1991). Measurement and simulation of the flow around a poppet valve. In Proc. 8th symp. turbulent shear flows (S. 13.2.1–13.2.6).
go back to reference Lilek, Ž., Schreck, E. & Perić, M. (1995). Parallelization of implicit methods for flow simulation. In S. G. Wagner (Hrsg.), Notes on numerical fluid mechanics (Bd. 50, S. 135–146). Braunschweig: Vieweg. Lilek, Ž., Schreck, E. & Perić, M. (1995). Parallelization of implicit methods for flow simulation. In S. G. Wagner (Hrsg.), Notes on numerical fluid mechanics (Bd. 50, S. 135–146). Braunschweig: Vieweg.
go back to reference Matheou, G. & Chung, D. (2014). Large-eddy simulation of stratified turbulence. Part II: Application of the stretched-vortex model to the atmospheric boundary layer. J. Atmos. Sci., 71, 4439–4460.ADSCrossRef Matheou, G. & Chung, D. (2014). Large-eddy simulation of stratified turbulence. Part II: Application of the stretched-vortex model to the atmospheric boundary layer. J. Atmos. Sci., 71, 4439–4460.ADSCrossRef
go back to reference McCormick, S. F. (Hrsg.). (1987). Multigrid methods. Philadelphia: Society for Industrial and Applied Mathematics (SIAM).MATH McCormick, S. F. (Hrsg.). (1987). Multigrid methods. Philadelphia: Society for Industrial and Applied Mathematics (SIAM).MATH
go back to reference Muzaferija, S. & Gosman, A. D. (1997). Finite-volume CFD procedure and adaptive error control strategy for grids of arbitrary topology. J. Comput. Physics, 138, 766–787.ADSMathSciNetCrossRef Muzaferija, S. & Gosman, A. D. (1997). Finite-volume CFD procedure and adaptive error control strategy for grids of arbitrary topology. J. Comput. Physics, 138, 766–787.ADSMathSciNetCrossRef
go back to reference Muzaferija, S. (1994). Adaptive finite volume method for flow predictions using unstructured meshes and multigrid approach (PhD Dissertation). University of London. Muzaferija, S. (1994). Adaptive finite volume method for flow predictions using unstructured meshes and multigrid approach (PhD Dissertation). University of London.
go back to reference Perić, M. & Schreck, E. (1995). Analysis of efficiency of implicit CFD methods on MIMD computers. Proc. Parallel CFD ’95 Conference. Perić, M. & Schreck, E. (1995). Analysis of efficiency of implicit CFD methods on MIMD computers. Proc. Parallel CFD ’95 Conference.
go back to reference Perić, M. (1993). Natural convection in trapezoidal cavities. Numer. Heat Transfer Part A (Applications), 24, 213–219. Perić, M. (1993). Natural convection in trapezoidal cavities. Numer. Heat Transfer Part A (Applications), 24, 213–219.
go back to reference Rakhimov, A. C., Visser, D. C. & Komen, E. M. J. (2018). Uncertainty quantification method for CFD applied to the turbulent mixing of two water layers. Nuclear Engrg. Design, 333, 1–15. Rakhimov, A. C., Visser, D. C. & Komen, E. M. J. (2018). Uncertainty quantification method for CFD applied to the turbulent mixing of two water layers. Nuclear Engrg. Design, 333, 1–15.
go back to reference Raw, M. J. (1995). A coupled algebraic multigrid method for the 3D Navier-Stokes equations. In W. Hackbusch & G. Wittum (Hrsg.), Fast solvers for flow problems, notes on numerical fluid mechanics (Bd. 49, S. 204–215). Braunschweig: Vieweg. Raw, M. J. (1995). A coupled algebraic multigrid method for the 3D Navier-Stokes equations. In W. Hackbusch & G. Wittum (Hrsg.), Fast solvers for flow problems, notes on numerical fluid mechanics (Bd. 49, S. 204–215). Braunschweig: Vieweg.
go back to reference Roache, P. J. (1994). Perspective: a method for uniform reporting of grid refinement studies. ASME J. Fluids Engrg., 116, 405–413.CrossRef Roache, P. J. (1994). Perspective: a method for uniform reporting of grid refinement studies. ASME J. Fluids Engrg., 116, 405–413.CrossRef
go back to reference Rodi, W., Bonnin, J.-C. & Buchal, T. (Hrsg.). (1995). Proc. ERCOFTAC workshop on data bases and testing of calculation methods for turbulent flows, April 3–7. Germany: Univ. Karlsruhe. Rodi, W., Bonnin, J.-C. & Buchal, T. (Hrsg.). (1995). Proc. ERCOFTAC workshop on data bases and testing of calculation methods for turbulent flows, April 3–7. Germany: Univ. Karlsruhe.
go back to reference Schalkwijk, J., Griffith, E., Post, F. H. & Jonker, H. J. J. (2012a). High-performance simulations of turbulent clouds on a desktop PC: Exploiting the GPU. Bull. Amer. Met. Soc., 93, 307–314.ADSCrossRef Schalkwijk, J., Griffith, E., Post, F. H. & Jonker, H. J. J. (2012a). High-performance simulations of turbulent clouds on a desktop PC: Exploiting the GPU. Bull. Amer. Met. Soc., 93, 307–314.ADSCrossRef
go back to reference Schreck, E. & Perić, M. (1993). Computation of fluid flow with a parallel multigrid solver. Int. J. Numer. Methods Fluids, 16, 303–327.ADSCrossRef Schreck, E. & Perić, M. (1993). Computation of fluid flow with a parallel multigrid solver. Int. J. Numer. Methods Fluids, 16, 303–327.ADSCrossRef
go back to reference Seidl, V. (1997). Entwicklung und Anwendung eines parallelen Finite-Volumen-Verfahrens zur Strömungssimulation auf unstrukturierten Gittern mit lokaler Verfeinerung (PhD Dissertation). University of Hamburg, Germany. Seidl, V. (1997). Entwicklung und Anwendung eines parallelen Finite-Volumen-Verfahrens zur Strömungssimulation auf unstrukturierten Gittern mit lokaler Verfeinerung (PhD Dissertation). University of Hamburg, Germany.
go back to reference Seidl, V., Perić, M. & Schmidt, S. (1996). Space- and time-parallel Navier-Stokes solver for 3D block-adaptive Cartesian grids. In A. Ecer, J. Periaux, N. Satofuka & S. Taylor (Hrsg.), Parallel Computational Fluid Dynamics 1995: Implementations and results using parallel computers (S. 577–584). North Holland – Elsevier. Seidl, V., Perić, M. & Schmidt, S. (1996). Space- and time-parallel Navier-Stokes solver for 3D block-adaptive Cartesian grids. In A. Ecer, J. Periaux, N. Satofuka & S. Taylor (Hrsg.), Parallel Computational Fluid Dynamics 1995: Implementations and results using parallel computers (S. 577–584). North Holland – Elsevier.
go back to reference Skamarock, W. C., Oliger, J. & Street, R. L. (1989). Adaptive grid refinement for numerical weather prediction. J. Comput. Phys., 80, 27–60. Skamarock, W. C., Oliger, J. & Street, R. L. (1989). Adaptive grid refinement for numerical weather prediction. J. Comput. Phys., 80, 27–60.
go back to reference Sullivan, P. P. & Patton, E. G. (2008). A highly parallel algorithm for turbulence simulations in planetary boundary layers: Results with meshes up to \(1024^{3}\). In 18th Conference on boundary layers and turbulence, AMS (S. Paper 11B.5, 11). Stockholm, Sweden. Sullivan, P. P. & Patton, E. G. (2008). A highly parallel algorithm for turbulence simulations in planetary boundary layers: Results with meshes up to \(1024^{3}\). In 18th Conference on boundary layers and turbulence, AMS (S. Paper 11B.5, 11). Stockholm, Sweden.
go back to reference Sullivan, P. P. & Patton, E. G. (2011). The effect of mesh resolution on convective boundary layer statistics and structures generated by large-eddy simulation. J. Atmos. Sci., 68, 2395–2415. Sullivan, P. P. & Patton, E. G. (2011). The effect of mesh resolution on convective boundary layer statistics and structures generated by large-eddy simulation. J. Atmos. Sci., 68, 2395–2415.
go back to reference Sunderam, V. S. (1990). PVM: a framework for parallel distributed computing. Concurrency and computaton: Practice and Experience, 2, 315–339.CrossRef Sunderam, V. S. (1990). PVM: a framework for parallel distributed computing. Concurrency and computaton: Practice and Experience, 2, 315–339.CrossRef
go back to reference Thompson, M. C. & Ferziger, J. H. (1989). A multigrid adaptive method for incompressible flows. J. Comput. Phys., 82, 94–121.ADSCrossRef Thompson, M. C. & Ferziger, J. H. (1989). A multigrid adaptive method for incompressible flows. J. Comput. Phys., 82, 94–121.ADSCrossRef
go back to reference Vanka, S. P. (1986). Block-implicit multigrid solution of Navier-Stokes equations in primitive variables. J. Comput. Phys, 65, 138–158.ADSMathSciNetCrossRef Vanka, S. P. (1986). Block-implicit multigrid solution of Navier-Stokes equations in primitive variables. J. Comput. Phys, 65, 138–158.ADSMathSciNetCrossRef
go back to reference Weiss, J. M., Maruszewski, J. P. & Smith, W. A. (1999). Implicit solution of preconditioned Navier-Stokes equations using algebraic multigrid. AIAA J., 37, 29–36.ADSCrossRef Weiss, J. M., Maruszewski, J. P. & Smith, W. A. (1999). Implicit solution of preconditioned Navier-Stokes equations using algebraic multigrid. AIAA J., 37, 29–36.ADSCrossRef
go back to reference Wesseling, P. (1990). Multigrid methods in computational fluid dynamics. ZAMM Z. Angew. Math. Mech., 70, T337–T347.MathSciNetCrossRef Wesseling, P. (1990). Multigrid methods in computational fluid dynamics. ZAMM Z. Angew. Math. Mech., 70, T337–T347.MathSciNetCrossRef
go back to reference Williams, J., Sarofeen, C., Shan, H. & Conley, M. (2016). An accelerated iterative linear solver with GPUs and CFD calculations of unstructured grids. Procedia Compu. Sci., 80, 1291–1300.CrossRef Williams, J., Sarofeen, C., Shan, H. & Conley, M. (2016). An accelerated iterative linear solver with GPUs and CFD calculations of unstructured grids. Procedia Compu. Sci., 80, 1291–1300.CrossRef
go back to reference Zhou, B., Simon, J. S. & Chow, F. K. (2014). The convective boundary layer in the Terra Incognita. J. Atmos. Sci., 71, 2547–2563.ADS Zhou, B., Simon, J. S. & Chow, F. K. (2014). The convective boundary layer in the Terra Incognita. J. Atmos. Sci., 71, 2547–2563.ADS
Metadata
Title
Steigerung der Effizienz und der Genauigkeit
Authors
Joel H. Ferziger
Milovan Perić
Robert L. Street
Copyright Year
2020
Publisher
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-662-46544-8_12

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