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We introduce a new regularized interface method for proving existence of weak solutions to nonlinear moving boundary problems with low-regularity interfaces. We study a fluid-poroelastic structure interaction (FPSI) problem coupling the…

Analysis of PDEs · Mathematics 2025-08-26 Jeffrey Kuan , Sunčica Čanić , Boris Muha

Poroelasticity describes the interaction of deformation and fluid flow in saturated porous media. A fully-mixed formulation of Biot's poroelasticity problem has the advantage of producing a better approximation of the Darcy velocity and…

Numerical Analysis · Mathematics 2025-04-25 Michele Botti , Daniele Prada , Anna Scotti , Michele Visinoni

In this work, we present a parametric finite element approximation of two-phase Navier-Stokes flow with viscoelasticity. The free boundary problem is given by the viscoelastic Navier-Stokes equations in the two fluid phases, connected by…

Numerical Analysis · Mathematics 2026-02-11 Harald Garcke , Robert Nürnberg , Dennis Trautwein

This paper studies a model of two-phase flow with an immersed material viscous interface and a finite element method for numerical solution of the resulting system of PDEs. The interaction between the bulk and surface media is characterized…

Numerical Analysis · Mathematics 2021-06-08 Maxim Olshanskii , Annalisa Quaini , Qi Sun

We present a priori error analysis for a fully discrete, parallelizable, explicit loosely coupled scheme for the time-dependent Stokes-Biot problem. The method decouples the fluid and poroelastic subproblems in a fully explicit fashion,…

Numerical Analysis · Mathematics 2026-03-24 Yifan Wang , Jeonghun Lee , Suncica Canic

We present a parametric finite element approximation of two-phase flow. This free boundary problem is given by the Navier--Stokes equations in the two phases, which are coupled via jump conditions across the interface. Using a novel…

Numerical Analysis · Mathematics 2015-06-02 John W. Barrett , Harald Garcke , Robert Nürnberg

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

In this work we analyze an optimized artificial fixed-stress iteration scheme for the numerical approximation of the Biot system modelling fluid flow in deformable porous media. The iteration is based on a prescribed constant artificial…

Numerical Analysis · Mathematics 2017-05-24 M. Bause , F. A. Radu , U. Köcher

Diffuse-interface theory provides a foundation for the modeling and simulation of microstructure evolution in a very wide range of materials, and for the tracking/capturing of dynamic interfaces between different materials on larger scales.…

Computational Physics · Physics 2018-08-03 Zhijie Xu , Paul Meakin , Alexandre Tartakovsky

This paper concerns a diffuse interface model for the flow of two incompressible viscoelastic fluids in a bounded domain. More specifically, the fluids are assumed to be macroscopically immiscible, but with a small transition region, where…

Analysis of PDEs · Mathematics 2024-11-15 Yadong Liu , Dennis Trautwein

This work proposes a mixed finite element method for the Biot poroelasticity equations that employs the lowest-order Raviart-Thomas finite element space for the solid displacement and piecewise constants for the fluid pressure. The method…

Numerical Analysis · Mathematics 2022-12-26 Wietse M. Boon , Alessio Fumagalli , Anna Scotti

We present a simple and efficient variational finite difference method for simulating time-dependent Stokes flow in the presence of irregular free surfaces and moving solid boundaries. The method uses an embedded boundary approach on…

Computational Physics · Physics 2011-05-25 Christopher Batty , Robert Bridson

We consider the dynamics of two-phase fluids, in particular the moving contact line, on a solid substrate. The dynamics are governed by the sharp-interface model consisting of the incompressible Navier-Stokes\slash Stokes equations with the…

Computational Physics · Physics 2020-07-15 Quan Zhao , Weiqing Ren

A deep understanding of the physical interactions between nanoparticles and target cell membranes is important in designing efficient nanocarrier systems for drug delivery applications. Here, we present a theoretical framework to describe…

Fluid Dynamics · Physics 2020-12-30 Abdallah Daddi-Moussa-Ider

A thermodynamic approach to rapid phase transformations within a diffuse interface in a binary system is developed. Assuming an extended set of independent thermodynamic variables formed by the union of the classic set of slow variables and…

Materials Science · Physics 2009-11-10 Peter Galenko , David Jou

We introduce and analyze a partially augmented fully-mixed formulation and a mixed finite element method for the coupled problem arising in the interaction between a free fluid and a poroelastic medium. The flows in the free fluid and…

Numerical Analysis · Mathematics 2023-05-02 Tongtong Li , Sergio Caucao , Ivan Yotov

We study the interaction between an incompressible, viscous, Newtonian fluid and a multilayered structure, which consists of a thin elastic layer and a thick poroelastic material. The thin layer is modeled using the linearly elastic Koiter…

Numerical Analysis · Mathematics 2013-08-22 Martina Bukac , Paolo Zunino , Ivan Yotov

In this paper, we propose a new formulation and a suitable finite element method for the steady coupling of viscous flow in deformable porous media using divergence-conforming filtration fluxes. The proposed method is based on the use of…

Numerical Analysis · Mathematics 2025-10-23 Ruben Caraballo , Chansophea Wathanak In , Alberto F. Martín , Ricardo Ruiz-Baier

This article presents a multi-physics methodology for the numerical simulation of physical systems that involve the non-linear interaction of multi-phase reactive fluids and elastoplastic solids, inducing high strain-rates and high…

Computational Physics · Physics 2021-06-04 Tim Wallis , Philip T. Barton , Nikolaos Nikiforakis

A diffused interface model describing the evolution of two conterminous incompressible fluids in a porous medium is discussed. The system consists of the Cahn-Hilliard equation with Flory-Huggins logarithmic potential, coupled via surface…

Analysis of PDEs · Mathematics 2024-07-24 Nitu Lakhmara , Hari Shankar Mahato