相关论文: Equations for two-phase flows: a primer

Two-dimensional potential flows of an ideal fluid with a free surface are considered in situations when shape of the bottom depends on time due to external reasons. Exact nonlinear equations describing surface waves in terms of the so…

In this paper a hyperbolic system of partial differential equations for two-phase mixture flows with $N$ components is studied. It is derived from a more complicated model involving diffusion and exchange terms. Important features of the…

This document is a presentation of the equations of simultaneous water and oil flow in deformable porous medium and linear poromechanics as well as the staggered solution algorithm to solve the coupled system of equations.

In this investigation we revisit the concept of "effective free surfaces" arising in the solution of the time-averaged fluid dynamics equations in the presence of free boundaries. This work is motivated by applications of the optimization…

The mass and momentum balances are theoretically studied in heterogeneous two-component systems. Following Gibbs the system is presented as two bulk and a single surface phases. Comparing the equations derived with some typical rheological…

We propose a general control framework for two-phase flows with variable densities in the diffuse interface formulation, where the distribution of the fluid components is described by a phase field. The flow is governed by the diffuse…

First we present an approach to formulate unbalanced three-phase power flow problems for general networks that explicitly separates device models and network models. A device model consists of (i) an internal model and (ii) a conversion…

We deal with a system of two coupled differential equations, describing the evolution of a first order phase transition. In particular, we have two non-linear parabolic equations: the first one is deduced from a balance law for entropy and…

The seven-equation model is a compressible multiphase formulation that allows for phasic velocity and pressure disequilibrium. These equations are solved using a diffused interface method that models resolved multiphase flows. Novel…

We consider a simplified model of a two-phase flow through a heterogeneous porous medium, in which the convection is neglected. This leads to a nonlinear degenerate parabolic problem in a domain shared in an arbitrary finite number of…

The explicit form of the interface equation of motion derived assuming a minimal surface is extended to general bicontinuous interfaces that appear in the diffusion limited stage of the phase separation process of binary mixtures. The…

Analytical/quasi-analytical solutions are proposed for a steady, compressible, two-phase flow in mechanical equilibrium in a rectilinear duct subjected to heating followed by cooling. The flow is driven by the pressure ratio between a…

We consider the governing equations for the motion of the inviscid fluids in two moving domains and an evolving surface from an energetic point of view. We employ our energetic variational approaches to derive inviscid multiphase flow…

Several aspects of the theory of the coexistence of phases and equilibrium forms are discussed. In section 1, the problem is studied from the point of view of thermodynamics. In section 2, the statistical mechanical theory is introduced. We…

The linear stability of stratified two-phase flows in rectangular ducts is studied numerically. The linear stability analysis takes into account all possible infinitesimal three-dimensional disturbances and is carried out by solution of the…

We present a new multiphase-field theory for describing pattern formation in multi-domain and/or multi-component systems. The construction of the free energy functional and the dynamic equations is based on criteria that ensure mathematical…

We prove the existence of generalized solution for incompressible and viscous non-Newtonian two-phase fluid flow for spatial dimension 2 and 3. The phase boundary moves along with the fluid flow plus its mean curvature while exerting…

We present a parametric finite element approximation of two-phase flow with insoluble surfactant. This free boundary problem is given by the Navier--Stokes equations for the two-phase flow in the bulk, which are coupled to the transport…

A diffuse interface (phase field) model for an electrochemical system is developed. We describe the minimal set of components needed to model an electrochemical interface and present a variational derivation of the governing equations. With…

In this article, we propose a novel conservative diffuse-interface method for the simulation of immiscible compressible two-phase flows. The proposed method discretely conserves the mass of each phase, momentum and total energy of the…