Cartesian grid methods for turbulent flow simulation in complex geometries Dröge, Marc Theodoor

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1 Cartesian grid methods for turbulent flow simulation in complex geometries Dröge, Marc Theodoor IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from it. Please check the document version below. Document Version Publisher's PDF, also known as Version of record Publication date: 2007 Link to publication in University of Groningen/UMCG research database Citation for published version (APA): Dröge, M. T. (2007). Cartesian grid methods for turbulent flow simulation in complex geometries s.n. Copyright Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons). Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Downloaded from the University of Groningen/UMCG research database (Pure): For technical reasons the number of authors shown on this cover page is limited to 10 maximum. Download date:

2 Cartesian Grid Methods for Turbulent Flow Simulation in Complex Geometries Marc Dröge

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4 RIJKSUNIVERSITEIT GRONINGEN Cartesian Grid Methods for Turbulent Flow Simulation in Complex Geometries Proefschrift ter verkrijging van het doctoraat in de Wiskunde en Natuurwetenschappen aan de Rijksuniversiteit Groningen op gezag van de Rector Magnificus, dr. F. Zwarts, in het openbaar te verdedigen op vrijdag 12 januari 2007 om uur door Marc Theodoor Dröge geboren op 23 maart 1977 te Groningen

5 Promotor: Copromotor: Prof. dr. A.E.P. Veldman Dr. ir. R.W.C.P. Verstappen Beoordelingscommissie: Prof. dr. ir. B.J. Geurts Prof. Dr.-Ing. M. Manhart Prof. dr. ir. P. Wesseling ISBN

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8 Contents 1 Introduction Simulation of turbulent flow Turbulence Direct Numerical Simulation Symmetry and conservation Numerical model Overview of numerical methods Symmetry-preserving finite volume discretisation Cartesian grid methods for flows in complex geometries Verification and validation Outline Mathematical Model Governing equations Boundary conditions Conservation properties Global conservation of momentum Global conservation of kinetic energy Numerical Model Geometry discretisation Cell and variable numbering Cut cells Conservation of momentum and kinetic energy Global conservation of momentum Global conservation of kinetic energy Mass conservation Convection Discretisation in uncut cells on a uniform grid Discretisation in uncut cells on a nonuniform grid Discretisation in cut cells on a nonuniform grid Boundary conditions for the convective operator Eigenvalue estimates of the convective operator Diffusion Standard discretisation on Cartesian grids Eigenvalues estimate of the diffusive operator

9 viii Contents Discretisation of a second-order derivative in 1D Discretisation of a second-order derivative in 2D Pressure gradient Time integration General aspects for time discretisation methods Time integration of the Navier-Stokes equation Pressure correction Solving the Poisson equation in Parallel Stability of time integration Simple Test Cases Smoothness results for various discretisations Flow through a channel skew to the grid Flow through a bent channel Flow Around a Circular Cylinder Flow around a circular cylinder at Re= Grid study Comparison with experiments Comparison with simulations Flow around a circular cylinder at Re= Flow around a circular cylinder at Re= Comparison with experiments Comparison with simulations Summary and Conclusions 107 Bibliography 111 Samenvatting 115 Dankwoord 121