Related papers: A fully discretization, unconditionally energy sta…
In this paper, we present a numerical scheme for the diffuse-interface model in [Abels, Garcke, Gr\"un, M3AS 22(3), 2012] for two-phase flow of immiscible, incompressible fluids. As that model is in particular consistent with…
In this paper, we focus on modeling and simulation of two-phase flow with moving contact lines and variable density. A thermodynamically consistent phase-field model with General Navier Boundary Condition is developed based on the concept…
The paper considers a thermodynamically consistent phase-field model of a two-phase flow of incompressible viscous fluids. The model allows for a non-linear dependence of fluid density on the phase-field order parameter. Driven by…
In this paper, we first establish a new fractional magnetohydrodynamic (MHD) coupled flow and heat transfer model for a generalized second-grade fluid. This coupled model consists of a fractional momentum equation and a heat conduction…
We develop finite element methods for coupling the steady-state Onsager--Stefan--Maxwell equations to compressible Stokes flow. These equations describe multicomponent flow at low Reynolds number, where a mixture of different chemical…
We propose a variational finite volume scheme to approximate the solutions to Wasserstein gradient flows. The time discretization is based on an implicit linearization of the Wasserstein distance expressed thanks to Benamou-Brenier formula,…
In this paper a time dependent Stokes problem that is motivated by a standard sharp interface model for the fluid dynamics of two-phase flows is studied. This Stokes interface problem has discontinuous density and viscosity coefficients and…
We propose and analyze two convection quasi-robust and pressure robust finite element methods for a fully nonlinear time-dependent magnetohydrodynamics problem. Both methods employ the $H_{\rm div}$ conforming BDM element coupled with an…
Convection-diffusion equations arise in a variety of applications such as particle transport, electromagnetics, and magnetohydrodynamics. Simulation of the convection-dominated regime for these problems, even with high-fidelity techniques,…
In this paper we analyze a fully discrete scheme for a general Cahn-Hilliard equation coupled with a nonsteady Magneto-hydrodynamics flow, which describes two immiscible, incompressible and electrically conducting fluids with different…
We present a finite element discretisation to model the interaction between a poroelastic structure and an elastic medium. The consolidation problem considers fully coupled deformations across an interface, ensuring continuity of…
In this paper, a thermal-dynamical consistent model for mass transfer across permeable moving interfaces is proposed by using the energy variation method. We consider a restricted diffusion problem where the flux across the interface…
We propose a novel structure preserving discretization for viscous and resistive magnetohydrodynamics. We follow the recent line of work on discrete least action principle for fluid and plasma equation, incorporating the recent advances to…
We are interested in the large-time behavior of solutions to finite volume discretizations of convection-diffusion equations or systems endowed with non-homogeneous Dirichlet and Neumann type boundary conditions. Our results concern various…
We present a novel asymptotic-preserving semi-implicit finite element method for weakly compressible and incompressible flows based on compatible finite element spaces. The momentum is sought in an $H(\mathrm{div})$-conforming space,…
In this paper, we introduce a new approach to solving the porous medium equation using a moving mesh finite element method that leverages the Onsager variational principle as an approximation tool. Both the continuous and discrete problems…
This article presents a new finite element method for convection-diffusion equations by enhancing the continuous finite element space with a flux space for flux approximations that preserve the important mass conservation locally on each…
We study a diffuse interface model for the flow of two viscous incompressible Newtonian fluids in a bounded domain. The fluids are assumed to be macroscopically immiscible, but a partial mixing in a small interfacial region is assumed in…
Direct numerical simulation of microscale fluid--structure interactions in multicomponent and multiphase flows requires methods that can represent moving boundaries together with fields constrained to evolving interfaces. Diffuse-domain…
We consider a sharp interface formulation for the multi-phase Mullins-Sekerka flow. The flow is characterized by a network of curves evolving such that the total surface energy of the curves is reduced, while the areas of the enclosed…