Related papers: A new Diffuse-interface approximation of the Willm…
Spatially extended systems, such as channel or pipe flows, are often equivariant under continuous symmetry transformations, with each state of the flow having an infinite number of equivalent solutions obtained from it by a translation or a…
We present accurate and mathematically consistent formulations of a diffuse-interface model for two-phase flow problems involving rapid evaporation. The model addresses challenges including discontinuities in the density field by several…
Understanding the relaxation of a system towards equilibrium is a longstanding problem in statistical mechanics. Here we address the role of long-range interactions in this process by considering a class of two-dimensional or geophysical…
We investigate a family of approximate multi-step proximal point methods, framed as implicit linear discretizations of gradient flow. The resulting methods are multi-step proximal point methods, with similar computational cost in each…
We analyze a one-component simple fluid in a liquid-vapor coexistence state, which forms an arbitrarily curved interface. By using an approach based on density functional theory, we obtain an exact and simple expression for the grand…
The Phase-Field Method (PFM) is employed to simulate two-phase flows with the fully-coupled Cahn-Hilliard-Navier-Stokes (CHNS) equations governing the temporal evolution. The methodology minimizes the total energy functional, accounting for…
We perform a non-linear analysis of a fluid-fluid wavy-stratified flow using a simplified two-fluid model, i.e., the fixed-flux model (FFM) which is an adaptation of shallow water theory for the two-layer problem. Linear analysis using the…
In this work, we first propose a diffuse interface model for simulating N phase flows with solid liquid phase change. In this model, a phase field approach is adopted to capture multiphase fluid interfaces, and an enthalpy based formulation…
We investigate two-phase flow in porous media and derive a two-scale model, which incorporates pore-scale phase distribution and surface tension into the effective behavior at the larger Darcy scale. The free-boundary problem at the pore…
A fully conservative sharp-interface method is developed for multiphase flows with phase change. The coupling between two phases is implemented via introducing the interfacial fluxes, which are obtained by solving a general Riemann problem…
This paper exploits the theory of geometric gradient flows to introduce an alternative regularization of the thin-film equation. The solution properties of this regularization are investigated via a sequence of numerical simulations whose…
In this paper, we mainly discuss the convergence behavior of diffuse domain method (DDM) for solving semilinear parabolic equations with Neumann boundary condition defined in general irregular domains. We use a phasefield function to…
We consider the simulation of barotropic flow of gas in long pipes and pipe networks. Based on a Hamiltonian reformulation of the governing system, a fully discrete approximation scheme is proposed using mixed finite elements in space and…
This work outlines a new three-dimensional diffuse interface finite volume method for the simulation of multiple solid and fluid components featuring large deformations, sliding and void opening. This is achieved by extending an existing…
We present a novel artificial diffusion method to circumvent the instabilities associated with the standard finite element approximation of convection-diffusion equations. Motivated by the micromorphic approach, we introduce an auxiliary…
In this paper, we address the challenge of accurately calculating droplet/bubble properties (e.g., volume, number) in diffuse-interface two-phase flow simulations. Currently, flood-fill algorithms can truncate a significant portion of the…
In this paper, we introduce a diffuse interface model for describing the dynamics of mixtures involving multiple (two or more) phases. The coupled hydrodynamical system is derived through an energetic variational approach. The total energy…
A complete analysis is presented for the far-field creeping flow produced by a multipolar force distribution in a fluid confined between two parallel planar walls. We show that at distances larger than several wall separations the flow…
In this paper, a regularity result for the Willmore flow is presented. It is established by means of a truncated translation technique in conjunction with the Implicit Function Theorem.
The flow near a moving contact line is primarily governed by three key parameters: viscosity ratio, dynamic contact angle, and inertia. While the behavior of dynamic contact angles has been extensively studied in earlier experimental and…