A theoretical and numerical model for the study of incompressible mixture flows

By Franck Boyer. 2002

246 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/81bc41a54d2061d26d886e61fcd479c97bcc1bbf

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In Applied Mathematics

In Computational Mechanics

In Materials Chemistry

Citations in the corpus

Thermodynamically Consistent, Frame Indifferent Diffuse Interface Models for Incompressible Two-Phase Flows with Different Densities (2011, methodology): “The further derivation of Boyer differs from the one in [12] and ours since the starting point are the equations for the conservation of linear momentum of each single fluid.”
A continuous surface tension force formulation for diffuse-interface models (2005, unknown): “In [3] [9] [12] [34], F 2 is used.”
The Cahn-Hilliard Equation with Logarithmic Potentials (2011, methodology): “We finally mention the coupling of the Cahn-Hilliard equation with the Navier-Stokes equations in the context of two-phase (multiphase) flows (see [1], [2], [28], [29], [30], [31], [33], [42], [55], [98], [99], [133], [137], [142], [145], [147], [155], [156], [213] and [215]).”
Benchmark computations of diffuse interface models for two‐dimensional bubble dynamics (2012, background): “Three of them, namely the models of Boyer [5], Ding et al.”
Phase-Field Models for Multi-Component Fluid Flows (2012, methodology): “In interface capturing methods such as level-set [24,78,79,85,91,92] and phase-field methods [4,6,13,29,46,47,54,56,74,86,90,102], the interface is implicitly captured by a contour of a particular scalar function.”
A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method (2003, unknown): “[3,9–11,25,28,33,36,46,48,53]).”
Cahn–Hilliard/Navier–Stokes Model for the Simulation of Three-Phase Flows (2010, methodology): “3 Coupling with the hydrodynamics To complete the modelling of three-phase incompressible flows, the Cahn-Hilliard system (5) is then coupled with Navier-Stokes equations (for more details see [3,4,11, 14]).”
Diffuse interface model for incompressible two-phase flows with large density ratios (2007, methodology): “An attempt to combine a rigorous approach for the derivation of the Cahn-Hilliard equation for solenoidal velocity fields with that of the Navier-Stokes equations has been presented by Boyer [21], but it involves several approximations for a specific flow configuration.”
Trajectory attractors for binary fluid mixtures in 3D (2010, background): “Systems like (1.1)–(1.4) in the case K = CH have been investigated in a number of papers (see, for instance, [ 12 , 13, 36, 39, 41, 46] ). However, confining ourselves to the most theoretical aspects (i.e., well-posedness, regularity, asymptotic behavior), to the best of our knowledge the first resu”
Study of a three component Cahn-Hilliard flow model (2006, unknown): “Diffuse interface models (see for instance the review in [2]) are now widely used to describe diphasic systems (see [6, 15, 28] and Sect.”
Two‐phase flows in karstic geometry (2014, methodology): “The Cahn-Hilliard-Stokes system can be viewed as the low Reynolds number approximation of the better-known Cahn-Hilliard-Navier-Stokes system for two phase flow [28, 35, 34, 36, 40, 66, 67, 68, 69, 70].”