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(2003)
Sobolev Spaces, second edition, volume
J. Barrett, H. Garcke, R. Nürnberg (2013)
A Stable Parametric Finite Element Discretization of Two-Phase Navier–Stokes FlowJournal of Scientific Computing, 63
H. Ding, P. Spelt, C. Shu (2007)
Diffuse interface model for incompressible two-phase flows with large density ratiosJ. Comput. Phys., 226
S. Hysing, S. Turek, D. Kuzmin, N. Parolini, E. Burman, Sashikumaar Ganesan, L. Tobiska (2009)
Quantitative benchmark computations of two‐dimensional bubble dynamicsInternational Journal for Numerical Methods in Fluids, 60
Naoto Kihara, H. Hanazaki, T. Mizuya, H. Ueda (2007)
Relationship between airflow at the critical height and momentum transfer to the traveling wavesPhysics of Fluids, 19
W. Drennan, M. Donelan, E. Terray, K. Katsaros (1996)
Oceanic Turbulence Dissipation Measurements in SWADEJournal of Physical Oceanography, 26
J. Bosch, M. Stoll, P. Benner (2014)
Fast solution of Cahn-Hilliard variational inequalities using implicit time discretization and finite elementsJ. Comput. Phys., 262
D. Kay, R. Welford (2006)
A multigrid finite element solver for the Cahn-Hilliard equationJ. Comput. Phys., 212
R. Verfürth (2010)
A posteriori error analysis of space-time finite element discretizations of the time-dependent Stokes equationsCalcolo, 47
Lian Shen, Xiang Zhang, D. Yue, M. Triantafyllou (2003)
Turbulent flow over a flexible wall undergoing a streamwise travelling wave motionJournal of Fluid Mechanics, 484
S. Aland, A. Voigt (2012)
Benchmark computations of diffuse interface models for two‐dimensional bubble dynamicsInternational Journal for Numerical Methods in Fluids, 69
P. Sullivan, J. McWilliams (2002)
Turbulent flow over water waves in the presence of stratificationPhysics of Fluids, 14
D. Kay, R. Welford (2007)
Efficient Numerical Solution of Cahn-Hilliard-Navier-Stokes Fluids in 2DSIAM J. Sci. Comput., 29
D. Wan, S. Turek (2007)
An efficient multigrid-FEM method for the simulation of solid-liquid two phase flowsJournal of Computational and Applied Mathematics, 203
J. McWilliams, P. Sullivan, C. Moeng (1997)
Langmuir turbulence in the oceanJournal of Fluid Mechanics, 334
P. Sullivan, J. McWilliams, C. Moeng (2000)
Simulation of turbulent flow over idealized water wavesJournal of Fluid Mechanics, 404
Christian Kahle (2015)
Simulation and Control of Two-Phase Flow Using Diffuse Interface Models
P. Clément (1975)
Approximation by finite element functions using local regularization, 9
Gonca Aki, W. Dreyer, J. Giesselmann, C. Kraus (2012)
A quasi-incompressible diffuse interface model with phase transitionMathematical Models and Methods in Applied Sciences, 24
Junseok Kim (2012)
Phase-Field Models for Multi-Component Fluid FlowsCommunications in Computational Physics, 12
S. Aland, J. Lowengrub, A. Voigt (2010)
Two-phase flow in complex geometries: A diffuse domain approach.Computer modeling in engineering & sciences : CMES, 57 1
D Anderson, G McFadden, A Wheeler (1997)
DIFFUSE-INTERFACE METHODS IN FLUID MECHANICSAnnual Review of Fluid Mechanics, 30
F. Boyer (2002)
A theoretical and numerical model for the study of incompressible mixture flowsComputers & Fluids, 31
M. Hintermüller, M. Hinze, Christian Kahle (2013)
An adaptive finite element Moreau-Yosida-based solver for a coupled Cahn-Hilliard/Navier-Stokes systemJ. Comput. Phys., 235
G. Grün, F. Klingbeil (2012)
Two-phase flow with mass density contrast: Stable schemes for a thermodynamic consistent and frame-indifferent diffuse-interface modelJ. Comput. Phys., 257
W. Tsai, Shi-ming Chen, G. Lu (2015)
Numerical Evidence of Turbulence Generated by Nonbreaking Surface WavesJournal of Physical Oceanography, 45
Tytti Saksa (2019)
Navier-Stokes EquationsFundamentals of Ship Hydrodynamics
C. Wunsch, R. Ferrari (2004)
VERTICAL MIXING, ENERGY, AND THE GENERAL CIRCULATION OF THE OCEANSAnnual Review of Fluid Mechanics, 36
P. Sullivan, J. McWilliams, W. Melville (2007)
Surface gravity wave effects in the oceanic boundary layer: large-eddy simulation with vortex force and stochastic breakersJournal of Fluid Mechanics, 593
V. Tsai, G. Ekström (2007)
Analysis of glacial earthquakesJournal of Geophysical Research, 112
G. Grün, F. Guillén-González, S. Metzger (2016)
On Fully Decoupled, Convergent Schemes for Diffuse Interface Models for Two-Phase Flow with General Mass DensitiesCommunications in Computational Physics, 19
J. Polton, Jerome Smith, J. MacKinnon, A. Tejada-Martínez (2008)
Rapid generation of high‐frequency internal waves beneath a wind and wave forced oceanic surface mixed layerGeophysical Research Letters, 35
H. Abels, Daniel Depner, H. Garcke (2012)
On an Incompressible Navier-Stokes/Cahn-Hilliard System with Degenerate MobilityarXiv: Analysis of PDEs
G. Grün (2013)
On Convergent Schemes for Diffuse Interface Models for Two-Phase Flow of Incompressible Fluids with General Mass DensitiesSIAM J. Numer. Anal., 51
S. Gross, A. Reusken (2011)
Numerical Methods for Two-phase Incompressible Flows
W. Tsai, Li-ping Hung (2007)
Three‐dimensional modeling of small‐scale processes in the upper boundary layer bounded by a dynamic ocean surfaceJournal of Geophysical Research, 112
A. James, J. Lowengrub (2004)
A surfactant-conserving volume-of-fluid method for interfacial flows with insoluble surfactantJournal of Computational Physics, 201
F. Boyer (1999)
Mathematical study of multi‐phase flow under shear through order parameter formulationAsymptotic Analysis, 20
H. Abels, Daniel Depner, H. Garcke (2011)
Existence of Weak Solutions for a Diffuse Interface Model for Two-Phase Flows of Incompressible Fluids with Different DensitiesJournal of Mathematical Fluid Mechanics, 15
H. Garcke, M. Hinze, Christian Kahle (2014)
A stable and linear time discretization for a thermodynamically consistent model for two-phase incompressible flowApplied Numerical Mathematics, 99
C. Eck (2005)
Homogenization of a Phase Field Model for Binary MixturesMultiscale Model. Simul., 3
H. Abels, H. Garcke, G. Grün (2011)
Thermodynamically Consistent, Frame Indifferent Diffuse Interface Models for Incompressible Two-Phase Flows with Different DensitiesarXiv: Fluid Dynamics
M. Benzi, G. Golub, J. Liesen (2005)
Numerical solution of saddle point problemsActa Numerica, 14
M. Hintermüller, M. Hinze, Moulay Tber (2011)
An adaptive finite-element Moreau–Yosida-based solver for a non-smooth Cahn–Hilliard problemOptimization Methods and Software, 26
Sashikumaar Ganesan, L. Tobiska (2009)
A coupled arbitrary Lagrangian-Eulerian and Lagrangian method for computation of free surface flows with insoluble surfactantsJ. Comput. Phys., 228
P. Sullivan, J. McWilliams (2010)
Dynamics of Winds and Currents Coupled to Surface WavesAnnual Review of Fluid Mechanics, 42
Xiaobing Feng (2006)
Fully Discrete Finite Element Approximations of the Navier-Stokes-Cahn-Hilliard Diffuse Interface Model for Two-Phase Fluid FlowsSIAM J. Numer. Anal., 44
F. Boyer, L. Chupin, P. Fabrie (2004)
Numerical study of viscoelastic mixtures through a Cahn–Hilliard flow modelEuropean Journal of Mechanics B-fluids, 23
P. Sutherland, W. Melville (2015)
Field Measurements of Surface and Near-Surface Turbulence in the Presence of Breaking WavesJournal of Physical Oceanography, 45
Zhenlin Guo, P. Lin, J. Lowengrub (2014)
A numerical method for the quasi-incompressible Cahn-Hilliard-Navier-Stokes equations for variable density flows with a discrete energy lawJ. Comput. Phys., 276
D. Kay, V. Styles, R. Welford (2008)
Finite element approximation of a Cahn−Hilliard−Navier−Stokes systemInterfaces and Free Boundaries, 10
J. Mellado, B. Stevens, H. Schmidt, N. Peters (2010)
Two-fluid formulation of the cloud-top mixing layer for direct numerical simulationTheoretical and Computational Fluid Dynamics, 24
J. Blowey, C. Elliott (1991)
The Cahn–Hilliard gradient theory for phase separation with non-smooth free energy Part II: Numerical analysisEuropean Journal of Applied Mathematics, 3
F. Boyer, C. Lapuerta, S. Minjeaud, B. Piar, M. Quintard (2010)
Cahn–Hilliard/Navier–Stokes Model for the Simulation of Three-Phase FlowsTransport in Porous Media, 82
J. Lowengrub, L. Truskinovsky (1998)
Quasi–incompressible Cahn–Hilliard fluids and topological transitionsProceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 454
O. Druzhinin, S. Elghobashi (1998)
DIRECT NUMERICAL SIMULATIONS OF BUBBLE-LADEN TURBULENT FLOWS USING THE TWO-FLUID FORMULATIONPhysics of Fluids, 10
L. Baňas, R. Nürnberg (2009)
A posteriori estimates for the Cahn-Hilliard equation with obstacle free energyMathematical Modelling and Numerical Analysis, 43
P. Lubin, S. Glockner (2015)
Numerical simulations of three-dimensional plunging breaking waves: generation and evolution of aerated vortex filamentsJournal of Fluid Mechanics, 767
D. Kay, D. Loghin, A. Wathen (2002)
A Preconditioner for the Steady-State Navier-Stokes EquationsSIAM J. Sci. Comput., 24
Long Chen (2008)
i FEM : AN INNOVATIVE FINITE ELEMENT METHOD PACKAGE IN MATLAB
[We propose to model physical effects at the sharp density interface between atmosphere and ocean with the help of diffuse interface approaches for multiphase flows with variable densities. We use the thermodynamical consistent variable density model proposed in Abels et al. (Mathematical Models and Methods in Applied Sciences 22:1150013, 2012). This results in a Cahn–Hilliard-/Navier–Stokes-type system which we complement with tangential Dirichlet boundary conditions to incorporate the effect of wind in the atmosphere. Wind is responsible for waves at the surface of the ocean, whose dynamics have an important impact on the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textit{CO}_{2}$$\end{document}—exchange between ocean and atmosphere. We tackle this mathematical model numerically with fully adaptive and integrated numerical schemes tailored to the simulation of variable density multiphase flows governed by diffuse interface models. Here, fully adaptive, integrated, efficient, and reliable means that the mesh resolution is chosen by the numerical algorithm according to a prescribed error tolerance in the a posteriori error control on the basis of residual-based error indicators, which allow to estimate the true error from below (efficient) and from above (reliable). Our approach is based on the work of Hintermüller et al. (Journal of Computational Physics 235:810–827, 2013), Garcke et al. (Applied Numerical Mathematics 99:151–171, 2016), where a fully adaptive efficient and reliable numerical method for the simulation of two-dimensional multiphase flows with variable densities is developed. In a first step, we incorporate the stimulation of surface waves via appropriate volume forcing.]
Published: Jan 24, 2019
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