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The numerical modelling of convection dominated high density ratio two-phase flow poses several challenges, amongst which is resolving the relatively thin shear layer at the interface. To this end we propose a sharp discretisation of the…

Numerical Analysis · Mathematics 2022-10-18 Ronald A. Remmerswaal , Arthur E. P. Veldman

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…

Computational Engineering, Finance, and Science · Computer Science 2024-11-04 Magdalena Schreter-Fleischhacker , Peter Munch , Nils Much , Martin Kronbichler , Wolfgang A. Wall , Christoph Meier

In this letter, we derive the sharp-interface limit of the Cahn-Hilliard-Biot equations using formal matched asymptotic expansions. We find that in each sub-domain, the quasi-static Biot equations are obtained with domain-specific material…

Analysis of PDEs · Mathematics 2024-12-06 Erlend Storvik , Carina Bringedal

We consider a time-dependent coupled Navier--Stokes/generalized poroelastic flow problem and propose a unified and monolithic finite element discretization based on implicit time stepping. To handle the fluid-structure interface we employ a…

Numerical Analysis · Mathematics 2026-05-19 Aparna Bansal , Nicolas A. Barnafi , Dwijendra Narain Pandey , Ricardo Ruiz-Baier

In this work, we investigate a nonconforming finite element approximation of phase-field parameterized topology optimization governed by the Stokes flow. The phase field, the velocity field and the pressure field are approximated by…

Numerical Analysis · Mathematics 2025-12-09 Bangti Jin , Jing Li , Yifeng Xu , Shengfeng Zhu

The viscous flow of two immiscible fluids in a porous medium on the Darcy scale is governed by a system of nonlinear parabolic equations. If infinite mobility of one phase can be assumed (e.g. in soil layers in contact with the atmosphere)…

Numerical Analysis · Mathematics 2021-06-29 David Seus , Florin A. Radu , Christian Rohde

In this paper, we present a novel approach to model the fluid/solid interaction forces in a direct solver of the Navier-Stokes equations based on the volume of fluid interface tracking method. The key ingredient of the model is the explicit…

Fluid Dynamics · Physics 2015-06-16 Kyle Mahady , Shahriar Afkhami , Lou Kondic

In this paper we apply the recently developed mimetic discretization method to the mixed formulation of the Stokes problem in terms of vorticity, velocity and pressure. The mimetic discretization presented in this paper and in [50] is a…

Numerical Analysis · Mathematics 2015-06-03 Jasper Kreeft , Marc Gerritsma

In this paper the development of a physically consistent phase-field theory of solidification shrinkage is presented. The coarse-grained hydrodynamic equations are derived directly from the N-body Hamiltonian equations in the framework of…

Materials Science · Physics 2020-02-28 Gyula I. Toth , Wenyue Ma

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…

Computational Physics · Physics 2020-06-11 Suhas S. Jain , Ali Mani , Parviz Moin

A diffuse-interface model for microstructure with an arbitrary number of components and phases was developed from basic thermodynamic and kinetic principles and formalized within a variational framework. The model includes a composition…

Materials Science · Physics 2011-07-28 Daniel A. Cogswell , W. Craig Carter

In this paper, we present a novel solution strategy for the Cahn-Hilliard-Biot model, a three-way coupled system that features the interplay of solid phase separation, fluid dynamics, and elastic deformations in porous media. It is a…

Numerical Analysis · Mathematics 2026-02-02 Cedric Riethmüller , Erlend Storvik

We introduce a stress/total-pressure formulation for poroelasticity that includes the coupling with steady nonlinear diffusion modified by stress. The nonlinear problem is written in mixed-primal form, coupling a perturbed twofold…

Numerical Analysis · Mathematics 2023-06-27 Bryan Gomez-Vargas , Kent-Andre Mardal , Ricardo Ruiz-Baier , Vegard Vinje

The interaction between thin structures and incompressible Newtonian fluids is ubiquitous both in nature and in industrial applications. In this paper we present an isogeometric formulation of such problems which exploits a boundary…

Numerical Analysis · Mathematics 2017-02-17 Luca Heltai , Josef Kiendl , Antonio DeSimone , Alessandro Reali

In this work, we present and analyze a fully-mixed finite element scheme for the dynamic poroelasticity problem in the low-frequency regime. We write the problem as a four-field, first-order, hyperbolic system of equations where the…

Numerical Analysis · Mathematics 2025-12-12 Stefano Bonetti , Michele Botti , Patrick Vega

Boundary integral numerical methods are among the most accurate methods for interfacial Stokes flow, and are widely applied. They have the advantage that only the boundary of the domain must be discretized, which reduces the number of…

Numerical Analysis · Mathematics 2021-05-18 David M. Ambrose , Michael Siegel , Keyang Zhang

We investigate the fluid-poroelastic structure interaction problem in a moving domain, governed by Navier-Stokes-Biot (NSBiot) system. First, we propose a fully parallelizable, loosely coupled scheme to solve the coupled system. At each…

Numerical Analysis · Mathematics 2024-09-25 Shihan Guo , Yizhong Sun , Yifan Wang , Xiaohe Yue , Haibiao Zheng

This paper concerns with finite element approximations of a quasi-static poroelasticity model in displacement-pressure formulation which describes the dynamics of poro-elastic materials under an applied mechanical force on the boundary. To…

Numerical Analysis · Mathematics 2014-12-01 Xiaobing Feng , Zhihao Ge , Yukun Li

Many physical systems of interest involve the close interaction of a flow in a domain with complex, time-varying boundaries. Treatment of boundaries of this nature is cumbersome due to the difficulty in explicitly tracking boundaries that…

Fluid Dynamics · Physics 2025-02-25 Emma M. Boyd , Eric Sandall , Maycon Meier , J. Matt Quinlan , Brandon Runnels

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…

Fluid Dynamics · Physics 2026-03-25 Jiangxu Huang , Chengjie Zhan , Zhenhua Chai , Changsheng Huang , Xi Liu