Computational Multiscale Methods for Turbulent Single and Two-Phase Flows

In this thesis, computational multiscale methods for turbulent single and two-phase flows are considered. For large-eddy simulation of turbulent single-phase incompressible flow, a novel approach based on multifractal subgrid-scale modeling is developed. Two-phase flows, where the interface separating the two fluids appears as a discontinuity in the flow field, are tackled by an extendend finite element method. The combined approach is applied to large-eddy simulation of turbulent two-phase flow.

[1]  Kenneth E. Jansen,et al.  A better consistency for low-order stabilized finite element methods , 1999 .

[2]  Jinhee Jeong,et al.  On the identification of a vortex , 1995, Journal of Fluid Mechanics.

[3]  Jean-François Remacle,et al.  A stabilized finite element method using a discontinuous level set approach for the computation of bubble dynamics , 2007, J. Comput. Phys..

[4]  Thomas J. R. Hughes,et al.  Large eddy simulation of turbulent channel flows by the variational multiscale method , 2001 .

[5]  Zhaoyuan Wang,et al.  A sharp surface tension modeling method for two‐phase incompressible interfacial flows , 2009 .

[6]  Thibaut Menard,et al.  Subgrid analysis of liquid jet atomization , 2011 .

[7]  A. Peirce Computer Methods in Applied Mechanics and Engineering , 2010 .

[8]  Arthur Veldman,et al.  Direct Numerical Simulation of Turbulence at Lower Costs , 1997 .

[9]  Heinz Pitsch,et al.  High order conservative finite difference scheme for variable density low Mach number turbulent flows , 2007, J. Comput. Phys..

[10]  Victor M. Calo,et al.  Residual-based multiscale turbulence modeling: Finite volume simulations of bypass transition , 2005 .

[11]  P. Moin,et al.  Direct numerical simulation of turbulent flow over a backward-facing step , 1997, Journal of Fluid Mechanics.

[12]  Prasad,et al.  Multifractal nature of the dissipation field of passive scalars in fully turbulent flows. , 1988, Physical review letters.

[13]  G. Kreiss,et al.  A conservative level set method for two phase flow II , 2005, Journal of Computational Physics.

[14]  Jungsoo Suh,et al.  Structures of turbulent open-channel flow in the presence of an air–water interface , 2012 .

[15]  T. Fries,et al.  On time integration in the XFEM , 2009 .

[16]  D. Pullin,et al.  A vortex-based subgrid stress model for large-eddy simulation , 1997 .

[17]  D. J. Lewis The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. II , 1950, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[18]  T. Coupez,et al.  Convected level set method for the numerical simulation of fluid buckling , 2011 .

[19]  Ted Belytschko,et al.  A finite element method for crack growth without remeshing , 1999 .

[20]  Thomas-Peter Fries,et al.  The stable XFEM for two-phase flows , 2013 .

[21]  U. Piomelli,et al.  Backward-facing step calculations using the shear improved Smagorinsky model , 2022 .

[22]  P. Moin,et al.  Numerical Simulation of Turbulent Flows , 1984 .

[23]  S. Osher,et al.  An improved level set method for incompressible two-phase flows , 1998 .

[24]  J. Domaradzki,et al.  The Subgrid-Scale Estimation Model , 1999 .

[25]  H. Baum,et al.  The Equations of Motion for Thermally Driven, Buoyant Flows. , 1978, Journal of research of the National Bureau of Standards.

[26]  P. Moin,et al.  A dynamic subgrid‐scale eddy viscosity model , 1990 .

[27]  D. Kuzmin,et al.  A minimization-based finite element formulation for interface-preserving level set reinitialization , 2013, Computing.

[28]  A. Reusken,et al.  A finite element based level set method for two-phase incompressible flows , 2006 .

[29]  Thomas J. R. Hughes,et al.  The multiscale formulation of large eddy simulation: Decay of homogeneous isotropic turbulence , 2001 .

[30]  N. Kasagi,et al.  Three-dimensional particle-tracking velocimetry measurement of turbulence statistics and energy budget in a backward-facing step flow , 1995 .

[31]  Thomas J. Hanratty,et al.  Turbulent mass transfer rates to a wall for large Schmidt numbers , 1977 .

[32]  G. Tryggvason Numerical simulations of the Rayleigh-Taylor instability , 1988 .

[33]  J. Smagorinsky,et al.  GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS , 1963 .

[34]  F. Xiao,et al.  LES of turbulent liquid jet primary breakup in turbulent coaxial air flow , 2014 .

[35]  Franck Nicoud,et al.  Conservative High-Order Finite-Difference Schemes for Low-Mach Number Flows , 2000 .

[36]  Volker Gravemeier,et al.  A VARIATIONAL MULTISCALE METHOD WITH MULTIFRACTAL SUBGRID-SCALE MODELING FOR LARGE-EDDY SIMULATION OF TURBULENT FLOW , 2014 .

[37]  C. W. Hirt,et al.  Volume of fluid (VOF) method for the dynamics of free boundaries , 1981 .

[38]  Gert Lube,et al.  Analysis of a variational multiscale method for Large-Eddy simulation and its application to homogeneous isotropic turbulence , 2010 .

[39]  Gregory C. Burton,et al.  Study of ultrahigh Atwood-number Rayleigh–Taylor mixing dynamics using the nonlinear large-eddy simulation method , 2011 .

[40]  Chunming Li,et al.  Distance Regularized Level Set Evolution and Its Application to Image Segmentation , 2010, IEEE Transactions on Image Processing.

[41]  T. Hughes,et al.  Isogeometric variational multiscale modeling of wall-bounded turbulent flows with weakly enforced boundary conditions on unstretched meshes , 2010 .

[42]  G. Tryggvason,et al.  A front-tracking method for viscous, incompressible, multi-fluid flows , 1992 .

[43]  J. Ferziger,et al.  Improved turbulence models based on large eddy simulation of homogeneous, incompressible, turbulent flows , 1983 .

[44]  Ian M. Mitchell,et al.  A hybrid particle level set method for improved interface capturing , 2002 .

[45]  S. Zalesak Fully multidimensional flux-corrected transport algorithms for fluids , 1979 .

[46]  A. Masud,et al.  A variational multiscale method for incompressible turbulent flows: Bubble functions and fine scale fields , 2011 .

[47]  S. McCormick,et al.  A multigrid tutorial (2nd ed.) , 2000 .

[48]  Deborah Greaves,et al.  Simulation of viscous water column collapse using adapting hierarchical grids , 2006 .

[49]  N. Adams,et al.  An approximate deconvolution procedure for large-eddy simulation , 1999 .

[50]  Wolfgang A. Wall,et al.  An isogeometric variational multiscale method for large-eddy simulation of coupled multi-ion transport in turbulent flow , 2013, J. Comput. Phys..

[51]  Wolfgang A. Wall,et al.  An algebraic variational multiscale-multigrid method based on plain aggregation for convection-diffusion problems , 2009 .

[52]  Gunilla Kreiss,et al.  A conservative level set method for two phase flow II , 2005, J. Comput. Phys..

[53]  F. Nicoud Numerical study of a channel flow with variable properties , 2022 .

[54]  Wolfgang A. Wall,et al.  An algebraic variational multiscale-multigrid method for large-eddy simulation of turbulent variable-density flow at low Mach number , 2010, J. Comput. Phys..

[55]  D. Lilly,et al.  A proposed modification of the Germano subgrid‐scale closure method , 1992 .

[56]  Gretar Tryggvason,et al.  Direct Numerical Simulations of Gas–Liquid Multiphase Flows: Preface , 2011 .

[57]  Yvonne Jaeger,et al.  Turbulence: An Introduction for Scientists and Engineers , 2015 .

[58]  T. Belytschko,et al.  An Extended Finite Element Method for Two-Phase Fluids , 2003 .

[59]  Kenneth Falconer,et al.  Fractal Geometry: Mathematical Foundations and Applications , 1990 .

[60]  T. Hughes Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods , 1995 .

[61]  L. Davidson,et al.  Large Eddy Simulation of Flow Past a Square Cylinder: Comparison of Different Subgrid Scale Models , 2000 .

[62]  Elias Balaras,et al.  A priori and a posteriori tests of inflow conditions for large-eddy simulation , 2004 .

[63]  Volker Gravemeier,et al.  Multifractal subgrid-scale modeling within a variational multiscale method for large-eddy simulation of turbulent flow , 2013, J. Comput. Phys..

[64]  Lewis F. Richardson,et al.  Weather Prediction by Numerical Process , 1922 .

[65]  Javier Jiménez,et al.  Scaling of the energy spectra of turbulent channels , 2003, Journal of Fluid Mechanics.

[66]  Delphine Lacanette,et al.  Parametric study of LES subgrid terms in a turbulent phase separation flow , 2010 .

[67]  Leonhard Kleiser,et al.  Subgrid‐scale energy transfer in the near‐wall region of turbulent flows , 1994 .

[68]  Taehun Lee,et al.  A level set characteristic Galerkin finite element method for free surface flows , 2005 .

[69]  Garth N. Wells,et al.  Erratum: "Conservation properties for the Galerkin and stabilised forms of the advection-diffusion and incompressible Navier-Stokes equations" (Computer Methods in Applied Mechanics and Engineering (2005) vol. 194 (1141-1159) 10.1016/j.cma.2004.06.034) , 2006 .

[70]  Volker John,et al.  On large Eddy simulation and variational multiscale methods in the numerical simulation of turbulent incompressible flows , 2006 .

[71]  R. Codina,et al.  Time dependent subscales in the stabilized finite element approximation of incompressible flow problems , 2007 .

[72]  Rainer Friedrich,et al.  ANALYSING TURBULENT BACKWARD-FACING STEP FLOW WITH THE LOWPASS-FILTERED NAVIER-STOKES EQUATIONS , 1990 .

[73]  R. LeVeque High-resolution conservative algorithms for advection in incompressible flow , 1996 .

[74]  T. Fries,et al.  The XFEM for high‐gradient solutions in convection‐dominated problems , 2009 .

[75]  Isao Kataoka,et al.  Turbulence structure of air-water bubbly flow—III. transport properties , 1975 .

[76]  John Kim,et al.  DIRECT NUMERICAL SIMULATION OF TURBULENT CHANNEL FLOWS UP TO RE=590 , 1999 .

[77]  O. Lebaigue,et al.  Jump conditions for filtered quantities at an under-resolved discontinuous interface. Part 2: A priori tests , 2009 .

[78]  Jensen,et al.  Fractal measures and their singularities: The characterization of strange sets. , 1987, Physical review. A, General physics.

[79]  Jean-Luc Guermond,et al.  Mathematical Perspectives on Large Eddy Simulation Models for Turbulent Flows , 2004 .

[80]  K. Sreenivasan FRACTALS AND MULTIFRACTALS IN FLUID TURBULENCE , 1991 .

[81]  T. Hughes,et al.  Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations , 1990 .

[82]  David Sondak,et al.  A residual based eddy viscosity model for the large eddy simulation of turbulent flows , 2014 .

[83]  S. Collis,et al.  Multiscale Methods for Turbulence Simulation and Control , 2002 .

[84]  Ramon Codina,et al.  The dissipative structure of variational multiscale methods for incompressible flows , 2010 .

[85]  C. Meneveau,et al.  Simple multifractal cascade model for fully developed turbulence. , 1987, Physical review letters.

[86]  Gregory C. Burton Scalar-energy spectra in simulations of Sc⪢1 mixing by turbulent jets using the nonlinear large-eddy simulation method , 2008 .

[87]  Frank Losasso,et al.  A fast and accurate semi-Lagrangian particle level set method , 2005 .

[88]  Volker John,et al.  A variational multiscale method for turbulent flow simulation with adaptive large scale space , 2010, J. Comput. Phys..

[89]  A. Reusken Analysis of an extended pressure finite element space for two-phase incompressible flows , 2008 .

[90]  Ann S. Almgren,et al.  An adaptive level set approach for incompressible two-phase flows , 1997 .

[91]  R. Sani,et al.  Incompressible Flow and the Finite Element Method, Volume 1, Advection-Diffusion and Isothermal Laminar Flow , 1998 .

[92]  T. Lund,et al.  Generation of Turbulent Inflow Data for Spatially-Developing Boundary Layer Simulations , 1998 .

[93]  M. Griebel,et al.  Numerical simulation of bubble and droplet deformation by a level set approach with surface tension in three dimensions , 2009 .

[94]  R. Pletcher,et al.  On the large eddy simulation of a turbulent channel flow with significant heat transfer , 1996 .

[95]  A. Yoshizawa Statistical theory for compressible turbulent shear flows, with the application to subgrid modeling , 1986 .

[96]  Richard Bellman,et al.  Effects of Surface Tension and Viscosity on Taylor Instability , 1954 .

[97]  Nicolas Moës,et al.  A stable Lagrange multiplier space for stiff interface conditions within the extended finite element method , 2009 .

[98]  Alvaro L. G. A. Coutinho,et al.  Stabilized edge‐based finite element simulation of free‐surface flows , 2007 .

[99]  Nikolaus A. Adams,et al.  An approximate deconvolution model for Lrge-Eddy Simulation of incompressible flows , 2001 .

[100]  A. Huerta,et al.  Finite Element Methods for Flow Problems , 2003 .

[101]  A. Oberai,et al.  Spectral analysis of the dissipation of the residual-based variational multiscale method , 2010 .

[102]  Gregory C. Burton,et al.  Multifractal subgrid-scale modeling for large-eddy simulation. II. Backscatter limiting and a posteriori evaluation , 2005 .

[103]  P. Moin,et al.  Effects of the Computational Time Step on Numerical Solutions of Turbulent Flow , 1994 .

[104]  Wolfgang A. Wall,et al.  Time-dependent subgrid scales in residual-based large eddy simulation of turbulent channel flow , 2010 .

[105]  David L. Chopp,et al.  A hybrid extended finite element/level set method for modeling phase transformations , 2002 .

[106]  Frederick Stern,et al.  An improved particle correction procedure for the particle level set method , 2009, J. Comput. Phys..

[107]  Marcus Herrmann,et al.  A sub-grid surface dynamics model for sub-filter surface tension induced interface dynamics , 2013 .

[108]  R. Lahey,et al.  Computation of incompressible bubble dynamics with a stabilized finite element level set method , 2005 .

[109]  Manuel V. Heitor,et al.  Measurements of turbulent and periodic flows around a square cross-section cylinder , 1988 .

[110]  Patrick Chassaing,et al.  The Modeling of Variable Density Turbulent Flows. A review of first-order closure schemes , 2001 .

[111]  Mark Sussman,et al.  An Efficient, Interface-Preserving Level Set Redistancing Algorithm and Its Application to Interfacial Incompressible Fluid Flow , 1999, SIAM J. Sci. Comput..

[112]  David M. Driver,et al.  Backward-facing step measurements at low Reynolds number, Re(sub h)=5000 , 1994 .

[113]  Parviz Moin,et al.  A dynamic global-coefficient subgrid-scale model for large-eddy simulation of turbulent scalar transport in complex geometries , 2009 .

[114]  Isao Kataoka,et al.  Turbulence structure of air-water bubbly flow—II. local properties , 1975 .

[115]  Klaus Bremhorst,et al.  Large-eddy simulation of heat transfer downstream of a backward-facing step , 2004 .

[116]  E. Puckett,et al.  A High-Order Projection Method for Tracking Fluid Interfaces in Variable Density Incompressible Flows , 1997 .

[117]  S. Collis,et al.  Monitoring unresolved scales in multiscale turbulence modeling , 2001 .

[118]  J A Sethian,et al.  A fast marching level set method for monotonically advancing fronts. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[119]  Isabelle Calmet,et al.  Large-eddy simulation of high-Schmidt number mass transfer in a turbulent channel flow , 1997 .

[120]  J. Andrzej Domaradzki,et al.  A subgrid-scale model for large-eddy simulation based on the physics of interscale energy transfer in turbulence , 2012 .

[121]  Nikolaus A. Adams,et al.  On improving mass conservation properties of the hybrid particle-level-set method , 2008 .

[122]  J. Nitsche Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind , 1971 .

[123]  P. Moin,et al.  A dynamic subgrid‐scale model for compressible turbulence and scalar transport , 1991 .

[124]  T. Belytschko,et al.  A review of extended/generalized finite element methods for material modeling , 2009 .

[125]  S. C. Luo,et al.  Effects of incidence and afterbody shape on flow past bluff cylinders , 1994 .

[126]  Frédéric Valentin,et al.  An unusual stabilized finite element method for a generalized Stokes problem , 2002, Numerische Mathematik.

[127]  W. Wall,et al.  An eXtended Finite Element Method/Lagrange multiplier based approach for fluid-structure interaction , 2008 .

[128]  Shadan Shahmiri A Hybrid Fixed-Grid-ALE Approach for Fluid-Structure Interaction , 2014 .

[129]  Benedikt Schott,et al.  A new face-oriented stabilized XFEM approach for 2D and 3D incompressible Navier–Stokes equations , 2014 .

[130]  John K. Eaton,et al.  Combined Heat Transfer and Fluid Dynamic Measurements Downstream of a Backward-Facing Step , 1985 .

[131]  Jean-François Remacle,et al.  A computational approach to handle complex microstructure geometries , 2003 .

[132]  Daniel Gaudlitz Numerische Untersuchung des Aufstiegsverhaltens von Gasblasen in Flüssigkeiten , 2008 .

[133]  Olivier Simonin,et al.  DNS of the interaction between a deformable buoyant bubble and a spatially decaying turbulence: A priori tests for LES two-phase flow modelling , 2008 .

[134]  Tom De Mulder,et al.  The role of bulk viscosity in stabilized finite element formulations for incompressible flow: A review , 1998 .

[135]  M. Sussman,et al.  A Coupled Level Set and Volume-of-Fluid Method for Computing 3D and Axisymmetric Incompressible Two-Phase Flows , 2000 .

[136]  Volker Gravemeier,et al.  The variational multiscale method for laminar and turbulent flow , 2006 .

[137]  Wolfgang A. Wall,et al.  An algebraic variational multiscale–multigrid method for large‐eddy simulation of turbulent pulsatile flows in complex geometries with detailed insight into pulmonary airway flow , 2013 .

[138]  E. D. Obasaju,et al.  An experimental study of pressure fluctuations on fixed and oscillating square-section cylinders , 1982, Journal of Fluid Mechanics.

[139]  Thomas J. R. Hughes,et al.  Finite element modeling of blood flow in arteries , 1998 .

[140]  C. Meneveau,et al.  The multifractal nature of turbulent energy dissipation , 1991, Journal of Fluid Mechanics.

[141]  Charles Meneveau,et al.  A fractal model for large eddy simulation of turbulent flow , 1999 .

[142]  G. Taylor The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I , 1950, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[143]  Nikolaus A. Adams,et al.  Direct modelling of subgrid scales of turbulence in large eddy simulations , 2002 .

[144]  James A. Sethian,et al.  THE DERIVATION AND NUMERICAL SOLUTION OF THE EQUATIONS FOR ZERO MACH NUMBER COMBUSTION , 1985 .

[145]  Volker John,et al.  A Finite Element Variational Multiscale Method for the Navier-Stokes Equations , 2005, SIAM J. Sci. Comput..

[146]  A. Coutinho,et al.  Simple finite element‐based computation of distance functions in unstructured grids , 2007 .

[147]  Pierre Sagaut,et al.  Numerical simulation of phase separation and a priori two-phase LES filtering , 2008 .

[148]  Wolfgang A. Wall,et al.  Residual‐based variational multiscale methods for laminar, transitional and turbulent variable‐density flow at low Mach number , 2011 .

[149]  D. Lakehal,et al.  Interface-turbulence interactions in large-scale bubbling processes , 2007 .

[150]  U. Schumann Subgrid Scale Model for Finite Difference Simulations of Turbulent Flows in Plane Channels and Annuli , 1975 .

[151]  G. Hulbert,et al.  A generalized-α method for integrating the filtered Navier–Stokes equations with a stabilized finite element method , 2000 .

[152]  H. G. E. Hentschel,et al.  The infinite number of generalized dimensions of fractals and strange attractors , 1983 .

[153]  Nikolaus A. Adams,et al.  Implicit subgrid-scale modeling for large-eddy simulation of passive-scalar mixing , 2007 .

[154]  Shmuel Einav,et al.  A laser-Doppler velocimetry study of ensemble-averaged characteristics of the turbulent near wake of a square cylinder , 1995, Journal of Fluid Mechanics.

[155]  M. Kronbichler,et al.  An algebraic variational multiscale-multigrid method for large eddy simulation of turbulent flow , 2010 .

[156]  Christopher E. Brennen,et al.  Fundamentals of Multiphase Flow , 2005 .

[157]  Gretar Tryggvason,et al.  Transition between regimes of a vertical channel bubbly upflow due to bubble deformability , 2013 .

[158]  Sanjiva K. Lele,et al.  Compressibility Effects on Turbulence , 1994 .

[159]  Ronald Fedkiw,et al.  A Boundary Condition Capturing Method for Multiphase Incompressible Flow , 2000, J. Sci. Comput..

[160]  Volker Gravemeier,et al.  Scale-separating operators for variational multiscale large eddy simulation of turbulent flows , 2006, J. Comput. Phys..

[161]  Isaac Harari,et al.  A bubble‐stabilized finite element method for Dirichlet constraints on embedded interfaces , 2007 .

[162]  Peter R. Voke,et al.  Flow Past a Square Cylinder: Test Case LES2 , 1997 .

[163]  Pierre Sagaut,et al.  Generation of synthetic turbulent inflow data for large eddy simulation of spatially evolving wall-bounded flows , 2009 .

[164]  P. Moin,et al.  Simulation of spatially evolving turbulence and the applicability of Taylor's hypothesis in compressible flow , 1992 .

[165]  Ramon Codina,et al.  Large eddy simulation of low Mach number flows using dynamic and orthogonal subgrid scales , 2014 .

[166]  Marian Brezina,et al.  Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems , 2005, Computing.

[167]  Kenneth E. Jansen,et al.  A stabilized finite element method for the incompressible Navier–Stokes equations using a hierarchical basis , 2001 .

[168]  S. Zaleski,et al.  Numerical simulation of droplets, bubbles and waves: state of the art , 2009 .

[169]  Wolfgang A. Wall,et al.  An algebraic variational multiscale-multigrid method for large-eddy simulation: generalized-α time integration, Fourier analysis and application to turbulent flow past a square-section cylinder , 2011 .

[170]  P. Sagaut,et al.  Boundary Conditions for Large-Eddy Simulation of Compressible Flows , 2009 .

[171]  Raymond S. Tuminaro,et al.  An algebraic multigrid approach to solve extended finite element method based fracture problems , 2013 .

[172]  Djamel Lakehal,et al.  Direct numerical simulation of turbulence in a sheared air–water flow with a deformable interface , 2003, Journal of Fluid Mechanics.

[173]  Dietrich Braess,et al.  Finite Elemente - Theorie, schnelle Löser und Anwendungen in der Elastizitätstheorie , 1992 .

[174]  Stéphane Popinet,et al.  A front-tracking algorithm for accurate representation of surface tension , 1999 .

[175]  Ronald Fedkiw,et al.  Level set methods and dynamic implicit surfaces , 2002, Applied mathematical sciences.

[176]  Gregory Charles Burton A multifractal subgrid-scale model for the large-eddy simulation of turbulent flows , 2003 .

[177]  T. Hughes,et al.  The variational multiscale method—a paradigm for computational mechanics , 1998 .

[178]  Jochen Fröhlich,et al.  LARGE EDDY SIMULATION OF VARIABLE DENSITY TURBULENT AXISYMMETRIC JETS , 2008, Proceeding of Fifth International Symposium on Turbulence and Shear Flow Phenomena.

[179]  W. Rodi,et al.  Closure Strategies for Turbulent and Transitional Flows: Introduction to Large Eddy Simulation of Turbulent Flows , 2002 .

[180]  P. Moin,et al.  Subgrid-scale backscatter in turbulent and transitional flows , 1991 .

[181]  Rolf Stenberg,et al.  On some techniques for approximating boundary conditions in the finite element method , 1995 .

[182]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[183]  Erik Burman,et al.  Numerical Approximation of Large Contrast Problems with the Unfitted Nitsche Method , 2011 .

[184]  André Massing,et al.  A Stabilized Nitsche Fictitious Domain Method for the Stokes Problem , 2012, J. Sci. Comput..

[185]  G. Batchelor,et al.  An Introduction to Fluid Dynamics , 1968 .

[186]  Robert Luce,et al.  A robust variant of NXFEM for the interface problem , 2012 .

[187]  R. A. Antonia,et al.  THE PHENOMENOLOGY OF SMALL-SCALE TURBULENCE , 1997 .

[188]  Carlo D'Angelo,et al.  Numerical approximation with Nitsche's coupling of transient Stokes'/Darcy's flow problems applied to hemodynamics , 2012 .

[189]  Thierry Poinsot,et al.  Quenching processes and premixed turbulent combustion diagrams , 1991, Journal of Fluid Mechanics.

[190]  P. Moin,et al.  Direct numerical study of air layer drag reduction phenomenon over a backward-facing step , 2011 .

[191]  A. Obukhov,et al.  Structure of Temperature Field in Turbulent Flow , 1970 .

[192]  I. Akkerman,et al.  Isogeometric analysis of free-surface flow , 2011, J. Comput. Phys..

[193]  Alex M. Andrew,et al.  Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science (2nd edition) , 2000 .

[194]  Ted Belytschko,et al.  Arbitrary discontinuities in finite elements , 2001 .

[195]  C. Meneveau,et al.  On the properties of similarity subgrid-scale models as deduced from measurements in a turbulent jet , 1994, Journal of Fluid Mechanics.

[196]  Werner J. A. Dahm,et al.  Experimental study of the fine-scale structure of conserved scalar mixing in turbulent shear flows. Part 1. Sc [Gt ] 1 , 1996, Journal of Fluid Mechanics.

[197]  R. Codina,et al.  Improving Eulerian two‐phase flow finite element approximation with discontinuous gradient pressure shape functions , 2005 .

[198]  Werner J. A. Dahm,et al.  Dual-plane stereo particle image velocimetry measurements of velocity gradient tensor fields in turbulent shear flow. I. Accuracy assessments , 2006 .

[199]  J. Koseff,et al.  A dynamic mixed subgrid‐scale model and its application to turbulent recirculating flows , 1993 .

[200]  P. Sagaut Large Eddy Simulation for Incompressible Flows , 2001 .

[201]  David R. Dowling,et al.  Experimental assessment of fractal scale similarity in turbulent flows. Part 3. Multifractal scaling , 1997, Journal of Fluid Mechanics.

[202]  Michael Manhart,et al.  DNS of passive scalar transport in turbulent channel flow at high Schmidt numbers , 2007 .

[203]  Jonathan J. Hu,et al.  ML 5.0 Smoothed Aggregation Users's Guide , 2006 .

[204]  O. Lebaigue,et al.  Jump conditions for filtered quantities at an under-resolved discontinuous interface. Part 1: Theoretical development , 2009 .

[205]  Marcel Lesieur,et al.  Large-eddy simulation applied to study the influence of upstream conditions on the time-dependant and averaged characteristics of a backward-facing step flow , 2007 .

[206]  Gretar Tryggvason,et al.  Dynamics of nearly spherical bubbles in a turbulent channel upflow , 2013, Journal of Fluid Mechanics.

[207]  P. Minev,et al.  A finite element technique for multifluid incompressible flow using Eulerian grids , 2003 .

[208]  Bernhard Müller,et al.  Low-Mach-Number Asymptotics of the Navier-Stokes Equations , 1998 .

[209]  Rainald Löhner,et al.  Improved error and work estimates for high‐order elements , 2013 .

[210]  A. W. Vreman The filtering analog of the variational multiscale method in large-eddy simulation , 2003 .

[211]  A. T. Fedorchenko A model of unsteady subsonic flow with acoustics excluded , 1997 .

[212]  Jack Chessa,et al.  An Enriched Finite Element Method for Axisymmetric Two-Phase Flow with Surface Tension' , 2013 .

[213]  K. Jansen,et al.  An evaluation of the variational multiscale model for large-eddy simulation while using a hierarchical basis , 2002 .

[214]  Helio J. C. Barbosa,et al.  The finite element method with Lagrange multiplier on the boundary: circumventing the Babuscka-Brezzi condition , 1991 .

[215]  Yoshihiko Oishi,et al.  Horizontal turbulent channel flow interacted by a single large bubble , 2014 .

[216]  Carlo Scalo,et al.  High-Schmidt-number mass transport mechanisms from a turbulent flow to absorbing sediments , 2012 .

[217]  Ramon Codina,et al.  Finite element approximation of turbulent thermally coupled incompressible flows with numerical sub-grid scale modeling , 2010 .

[218]  I. Babuska The finite element method with Lagrangian multipliers , 1973 .

[219]  C. Meneveau,et al.  Scale-Invariance and Turbulence Models for Large-Eddy Simulation , 2000 .

[220]  M. Germano,et al.  Turbulence: the filtering approach , 1992, Journal of Fluid Mechanics.

[221]  S. Zaleski,et al.  DIRECT NUMERICAL SIMULATION OF FREE-SURFACE AND INTERFACIAL FLOW , 1999 .

[222]  D. Sharp An overview of Rayleigh-Taylor instability☆ , 1984 .

[223]  Thomas J. Hanratty,et al.  Transport of a passive scalar in a turbulent channel flow , 1997 .

[224]  Charbel Farhat,et al.  A Variational Multiscale Method for the Large Eddy Simulation of Compressible Turbulent Flows on Unstructured Meshes - Application to vortex shedding , 2004 .

[225]  Wolfgang A. Wall,et al.  An accurate, robust, and easy-to-implement method for integration over arbitrary polyhedra: Application to embedded interface methods , 2014, J. Comput. Phys..

[226]  G. Batchelor Small-scale variation of convected quantities like temperature in turbulent fluid Part 1. General discussion and the case of small conductivity , 1959, Journal of Fluid Mechanics.

[227]  K. Jansen,et al.  On the interaction between dynamic model dissipation and numerical dissipation due to streamline upwind/Petrov–Galerkin stabilization , 2005 .

[228]  W. Wall,et al.  A face‐oriented stabilized Nitsche‐type extended variational multiscale method for incompressible two‐phase flow , 2015 .

[229]  Erik Burman,et al.  Interior penalty variational multiscale method for the incompressible Navier-Stokes equation: Monitoring artificial dissipation , 2007 .

[230]  Jintai Chung,et al.  A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method , 1993 .

[231]  B. Mandelbrot Intermittent turbulence in self-similar cascades : divergence of high moments and dimension of the carrier , 2004 .

[232]  Thomas-Peter Fries,et al.  The extended finite element method for two-phase and free-surface flows: A systematic study , 2011, J. Comput. Phys..

[233]  Mark Sussman,et al.  A sharp interface method for incompressible two-phase flows , 2007, J. Comput. Phys..

[234]  J. Szmelter Incompressible flow and the finite element method , 2001 .

[235]  J. Douglas,et al.  Interior Penalty Procedures for Elliptic and Parabolic Galerkin Methods , 1976 .

[236]  T. Hughes,et al.  Large Eddy Simulation and the variational multiscale method , 2000 .

[237]  Andreas Zilian,et al.  The enriched space–time finite element method (EST) for simultaneous solution of fluid–structure interaction , 2008 .

[238]  Gregory C. Burton,et al.  The nonlinear large-eddy simulation method applied to Sc≈1 and Sc⪢1 passive-scalar mixing , 2008 .

[239]  Gregory C. Burton,et al.  Multifractal subgrid-scale modeling for large-eddy simulation. I. Model development and a priori testing , 2005 .

[240]  B. Lee The effect of turbulence on the surface pressure field of a square prism , 1975, Journal of Fluid Mechanics.

[241]  Richard H. Pletcher,et al.  LARGE EDDY SIMULATION OF THE TURBULENT FLOW PAST A BACKWARD FACING STEP WITH HEAT TRANSFER AND PROPERTY VARIATIONS , 2002, Proceeding of Second Symposium on Turbulence and Shear Flow Phenomena.

[242]  P. Hansbo,et al.  A cut finite element method for a Stokes interface problem , 2012, 1205.5684.

[243]  J. Lumley,et al.  A First Course in Turbulence , 1972 .

[244]  Parviz Moin,et al.  ADVANCES IN LARGE EDDY SIMULATION METHODOLOGY FOR COMPLEX FLOWS , 2002, Proceeding of Second Symposium on Turbulence and Shear Flow Phenomena.

[245]  Djamel Lakehal,et al.  Subgrid-scale modelling of surface tension within interface tracking-based Large Eddy and Interface Simulation of 3D interfacial flows , 2012 .

[246]  Wolfgang A. Wall,et al.  Towards a taxonomy for multiscale methods in computational mechanics: building blocks of existing methods , 2007 .

[247]  Emanuele Schiavi,et al.  Multigrid methods and automatic segmentation: an application to CT images of the liver , 2007 .

[248]  Peter Gamnitzer,et al.  Residual-based variational multiscale methods for turbulent flows and fluid-structure interaction , 2010 .

[249]  Z. Warhaft Passive Scalars in Turbulent Flows , 2000 .

[250]  P. Hansbo,et al.  A Nitsche extended finite element method for incompressible elasticity with discontinuous modulus of elasticity , 2009 .

[251]  A. Yaglom,et al.  Heat and mass transfer laws for fully turbulent wall flows , 1972 .

[252]  Pierre Sagaut,et al.  Towards large eddy simulation of isothermal two-phase flows: Governing equations and a priori tests , 2007 .

[253]  Parviz Moin,et al.  TACKLING TURBULENCE WITH SUPERCOMPUTERS , 1997 .

[254]  Nikolaus A. Adams,et al.  On implicit subgrid-scale modeling in wall-bounded flows , 2007 .

[255]  I. Babuska,et al.  Stable Generalized Finite Element Method (SGFEM) , 2011, 1104.0960.

[256]  Katepalli R. Sreenivasan,et al.  New results on the fractal and multifractal structure of the large Schmidt number passive scalars in fully turbulent flows , 1989 .

[257]  S. Osher,et al.  A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method) , 1999 .

[258]  S. Osher,et al.  Spatially adaptive techniques for level set methods and incompressible flow , 2006 .

[259]  Peter J. Mucha,et al.  A narrow-band gradient-augmented level set method for multiphase incompressible flow , 2014, J. Comput. Phys..

[260]  Ugo Piomelli,et al.  Large-eddy simulation: achievements and challenges , 1999 .

[261]  Charles Meneveau,et al.  Germano identity-based subgrid-scale modeling: A brief survey of variations on a fertile theme , 2012 .

[262]  Ted Belytschko,et al.  Elastic crack growth in finite elements with minimal remeshing , 1999 .

[263]  Roland Becker,et al.  Mesh adaptation for Dirichlet flow control via Nitsche's method , 2002 .

[264]  P. Woodward,et al.  SLIC (Simple Line Interface Calculation) , 1976 .

[265]  Richard Pasquetti,et al.  Experimental and high-order LES analysis of the flow in near-wall region of a square cylinder , 2011 .

[266]  S. Osher,et al.  A level set approach for computing solutions to incompressible two-phase flow , 1994 .

[267]  Elias Balaras,et al.  Inflow conditions for large-eddy simulations of mixing layers , 1999 .

[268]  S. Corrsin On the Spectrum of Isotropic Temperature Fluctuations in an Isotropic Turbulence , 1951 .

[269]  A. Kolmogorov The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers , 1991, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[270]  A. Leonard Energy Cascade in Large-Eddy Simulations of Turbulent Fluid Flows , 1975 .

[271]  M. Quecedo,et al.  Application of the level set method to the finite element solution of two-phase flows , 2001 .

[272]  Gavin Tabor,et al.  Inlet conditions for large eddy simulation: A review , 2010 .

[273]  Wolfgang Rodi,et al.  The flapping shear layer formed by flow separation from the forward corner of a square cylinder , 1994, Journal of Fluid Mechanics.

[274]  Arnold Reusken,et al.  An extended pressure finite element space for two-phase incompressible flows with surface tension , 2007, J. Comput. Phys..