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For a two phase incompressible flow we consider a diffuse interface model aimed at addressing the movement of three-phase (fluid-fluid-solid) contact lines. The model consists of the Cahn Hilliard Navier Stokes system with a variant of the Navier slip boundary conditions. We show that this model possesses a natural energy law. For this system, a new numerical technique based on operator splitting and fractional time-stepping is proposed. The method is shown to be unconditionally stable. We present...
In this short note we correct a conceptual error in the
heuristic derivation of a kinetic equation used for the
description of a one-dimensional granular medium in the so
called quasi-elastic limit, presented by the same authors in
reference[1]. The equation we derived is however correct so that,
the rigorous analysis on this equation, which constituted the
main purpose of that paper, remains unchanged.
The study of the fluctuations in the steady state of a heated granular system is
reviewed. A Boltzmann-Langevin description can be built requiring consistency with the
equations for the one- and two-particle correlation functions. From the Boltzmann-Langevin
equation, Langevin equations for the total energy and the transverse velocity field are
derived. The existence of a fluctuation-dissipation relation for the transverse velocity
field is also...
Two-phase fluid flows on substrates (i.e. wetting phenomena) are important in many industrial processes, such as micro-fluidics and coating flows. These flows include additional physical effects that occur near moving (three-phase) contact lines. We present a new 2-D variational (saddle-point) formulation of a Stokesian fluid with surface tension that interacts with a rigid substrate. The model is derived by an Onsager type principle using shape differential calculus (at the sharp-interface, front-tracking...
The high shear rate thrombus formation was only recently recognized as another way of thrombosis. Models proposed in Weller (2008), (2010) take into account this type of thrombosis. This work uses the phase-field method to model these evolving interface problems. A loosely coupled iterative procedure is introduced to solve the coupled system of equations. Convergence behavior on two levels of refinement of perfusion chamber geometry and cylinder geometry is then studied. The perfusion chamber simulations...
We construct an approximate Riemann solver for the isentropic Baer−Nunziato two-phase flow model, that is able to cope with arbitrarily small values of the statistical phase fractions. The solver relies on a relaxation approximation of the model for which the Riemann problem is exactly solved for subsonic relative speeds. In an original manner, the Riemann solutions to the linearly degenerate relaxation system are allowed to dissipate the total energy in the vanishing phase regimes, thereby enforcing...
We study a depth-averaged model of gravity-driven flows made of
solid grains and fluid, moving over variable basal surface.
In particular, we are interested in applications
to geophysical flows such as avalanches and debris flows,
which typically contain both solid material and interstitial fluid.
The model system consists of mass and momentum balance equations for the
solid and fluid components, coupled together by both
conservative and non-conservative terms involving the derivatives of the...
The aim of this paper is to present a method using both the ideas of sectional approach and moment methods in order to accurately simulate evaporation phenomena in gas-droplets flows. Using the underlying kinetic interpretation of the sectional method [Y. Tambour, Combust. Flame 60 (1985) 15–28] exposed in [F. Laurent and M. Massot, Combust. Theory Model. 5 (2001) 537–572], we propose an extension of this approach based on a more accurate representation of the droplet size number density in each...
The aim of this paper is to present a method using both the ideas of sectional
approach and moment methods in order to accurately simulate evaporation
phenomena in gas-droplets flows. Using the underlying kinetic interpretation of
the sectional method [Y. Tambour, Combust. Flame60 (1985)
15–28] exposed in [F. Laurent and M. Massot, Combust. Theory
Model.5 (2001) 537–572], we propose an extension of this
approach based on a more accurate representation of the droplet size number
density in each...
The paper is devoted to the computation of two-phase flows in a porous medium
when applying the two-fluid approach.
The basic formulation is presented first, together with the main properties
of the model. A few basic analytic solutions are then provided, some of them corresponding
to solutions of the one-dimensional Riemann problem.
Three distinct Finite-Volume schemes are then introduced. The first two schemes, which rely on the Rusanov scheme,
are shown to give wrong approximations in some...
We consider a continuum model describing steady flows of a miscible mixture of two fluids. The densities of the fluids and their velocity fields are prescribed at infinity: , . Neglecting the convective terms, we have proved earlier that weak solutions to such a reduced system exist. Here we establish a uniqueness type result: in the absence of the external forces and interaction terms, there is only one such solution, namely , , .
In this paper, we first construct a model for free surface flows that takes into account the air entrainment by a system of four partial differential equations. We derive it by taking averaged values of gas and fluid velocities on the cross surface flow in the Euler equations (incompressible for the fluid and compressible for the gas). The obtained system is conditionally hyperbolic. Then, we propose a mathematical kinetic interpretation of this system to finally construct a two-layer kinetic scheme...
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