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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…

Numerical Analysis · Mathematics 2012-10-19 Günther Grün , Fabian Klingbeil

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…

Numerical Analysis · Mathematics 2020-01-29 Lingyue Shen , Huaxiong Huang , Ping Lin , Zilong Song , Shixin Xu

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…

Numerical Analysis · Mathematics 2023-09-27 Yerbol Palzhanov , Alexander Zhiliakov , Annalisa Quaini , Maxim Olshanskii

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…

Numerical Analysis · Mathematics 2022-11-29 Xiaoqing Chi , Hui Zhang , Xiaoyun Jiang

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…

Numerical Analysis · Mathematics 2022-09-26 Francis R. A. Aznaran , Patrick E. Farrell , Charles W. Monroe , Alexander J. Van-Brunt

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,…

Numerical Analysis · Mathematics 2019-07-22 Clément Cancès , Thomas O. Gallouët , Gabriele Todeschi

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…

Numerical Analysis · Mathematics 2018-07-12 Igor Voulis , Arnold Reusken

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…

Numerical Analysis · Mathematics 2025-06-12 L. Beirão da Veiga , F. Dassi , G. Vacca

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,…

Numerical Analysis · Mathematics 2023-05-24 James H. Adler , Casey Cavanaugh , Xiaozhe Hu , Andy Huang , Nathaniel Trask

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…

Numerical Analysis · Mathematics 2022-02-04 Hailong Qiu

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…

Numerical Analysis · Mathematics 2023-06-21 S. Badia , M. Hornkjøl , A. Khan , K. -A. Mardal , A. F. Martín , R. Ruiz-Baier

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…

Numerical Analysis · Mathematics 2022-06-15 Yuzhe Qin , Huaxiong Huang , Yi Zhu , Chun Liu , Shixin Xu

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…

Numerical Analysis · Mathematics 2025-04-09 Valentin Carlier

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…

Analysis of PDEs · Mathematics 2018-10-03 Claire Chainais-Hillairet , Maxime Herda

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,…

Numerical Analysis · Mathematics 2024-07-16 Enrico Zampa , Michael Dumbser

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…

Numerical Analysis · Mathematics 2024-04-01 Si Xiao , Xianmin Xu

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…

Numerical Analysis · Mathematics 2017-10-24 Yujie Liu , Junping Wang , Qingsong Zou

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…

Analysis of PDEs · Mathematics 2011-04-01 Helmut Abels

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…

Biological Physics · Physics 2026-05-14 Xinpeng Xu

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…

Numerical Analysis · Mathematics 2024-07-29 Tokuhiro Eto , Harald Garcke , Robert Nürnberg