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The elastic energy of a bending-resistant interface depends both on its geometry and its material composition. We consider such a heterogeneous interface in the plane, modeled by a curve equipped with an additional density function. The…

Analysis of PDEs · Mathematics 2024-07-02 Anna Dall'Acqua , Gaspard Jankowiak , Leonie Langer , Fabian Rupp

We analyze numerical approximations for axisymmetric two-phase flow in the arbitrary Lagrangian-Eulerian (ALE) framework. We consider a parametric formulation for the evolving fluid interface in terms of a one-dimensional generating curve.…

Numerical Analysis · Mathematics 2023-12-25 Harald Garcke , Robert Nürnberg , Quan Zhao

The formal sharp-interface asymptotics in a degenerate Cahn-Hilliard model for viscoelastic phase separation with cross-diffusive coupling to a bulk stress variable are shown to lead to non-local lower-order counterparts of the classical…

Analysis of PDEs · Mathematics 2026-05-22 Katharina Hopf , John King , Andreas Münch , Barbara Wagner

The finite element simulation of dynamic wetting phenomena, requiring the computation of flow in a domain confined by intersecting a liquid-fluid free surface and a liquid-solid interface, with the three-phase contact line moving across the…

Computational Physics · Physics 2012-02-20 J. E. Sprittles , Y. D. Shikhmurzaev

We present a systematic derivation of the gradient flows associated to a broad class of interfacial energies, emphasizing the relation between intrinsic and extrinsic variations of the interface. We show that the intrinsic variables…

Analysis of PDEs · Mathematics 2025-01-28 Vinh Nguyen , Keith Promislow , Brian Wetton

In this work, we study a phase-field model for curvature-driven pattern formation in biomembranes. The model is derived as a gradient flow of an energy functional that approximates the two-phase Canham--Helfrich energy. This leads to a…

Analysis of PDEs · Mathematics 2025-11-27 Patrik Knopf , Anastasija Pešić , Dennis Trautwein

We revisit the sharp-interface continuum thermodynamics of two-phase multicomponent fluid systems, accounting for partial mass and partial momentum balances both in the bulk phases and on the interface. This allows to describe the transfer…

Fluid Dynamics · Physics 2025-02-21 Dieter Bothe

A comprehensive scheme for the spatial discretisation of continuity equation, momentum advection and normal and shear stresses at the fluid interfaces is presented for numerically simulating the incompressible two phase flows based on the…

Fluid Dynamics · Physics 2014-08-11 Jun-De Li

We consider two-layers of immiscible liquids confined between an upper and a lower rigid plate. The dynamics of the free liquid-liquid interface is described for arbitrary amplitudes by a single evolution equation derived from the basic…

Pattern Formation and Solitons · Physics 2007-05-23 D. Merkt , A. Pototsky , M. Bestehorn , U. Thiele

Two phase flows that include phase transition, especially phase creation, with a sharp interface remain a challenging task for numerics. We consider the isothermal Euler equations with phase transition between a liquid and a vapor phase.…

Numerical Analysis · Mathematics 2022-11-03 Sandra May , Ferdinand Thein

This work has explored interface evolution and pinch-off mechanism of the droplet formation in two-phase flow through cross-flow microfluidic device. The two-dimensional mathematical model equations have been solved using the finite element…

Fluid Dynamics · Physics 2022-03-10 Akepogu Venkateshwarlu , Ram Prakash Bharti

In this paper, we propose and analyze a diffuse interface model for inductionless magnetohydrodynamic fluids. The model couples a convective Cahn-Hilliard equation for the evolution of the interface, the Navier-Stokes system for fluid flow…

Analysis of PDEs · Mathematics 2023-12-20 Xiaodi Zhang

A novel finite element framework is proposed for the numerical simulation of two phase flows with surface tension. The Level-Set (LS) method with piece-wise quadratic (P2) interpolation for the liquid-gas interface is used in order to reach…

Computational Engineering, Finance, and Science · Computer Science 2020-10-27 Modesar Shakoor , Chung Hae Park

In this paper, we consider the sharp interface limit of a matrix-valued Allen-Cahn equation, which takes the form: $$\partial_t A=\Delta A-\varepsilon^{-2}( A A^{\mathrm{T}}A-…

Analysis of PDEs · Mathematics 2021-06-16 Mingwen Fei , Fanghua Lin , Wei Wang , Zhifei Zhang

We propose a new unfitted finite element method for simulation of two-phase flows in presence of insoluble surfactant. The key features of the method are 1) discrete conservation of surfactant mass; 2) the possibility of having meshes that…

Numerical Analysis · Mathematics 2022-11-30 Thomas Frachon , Sara Zahedi

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

An evolving surface finite element discretisation is analysed for the evolution of a closed two-dimensional surface governed by a system coupling a generalised forced mean curvature flow and a reaction--diffusion process on the surface,…

Numerical Analysis · Mathematics 2022-06-06 Charles M. Elliott , Harald Garcke , Balázs Kovács

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

We present a Cartesian cut-cell finite-volume method for sharp-interface two-phase diffusion problems in static geometries. The formulation follows a two-fluid approach: independent diffusion equations are discretized in each phase on a…

Numerical Analysis · Mathematics 2026-01-07 Louis Libat , Can Selçuk , Eric Chénier , Vincent Le Chenadec

This paper presents a finite volume method for simulating two-phase flows using a level set approach coupled with volume of fluid method capable of simulating sharp fluid interfaces. The efficiency of the method is a result of the fact that…

Computational Physics · Physics 2022-07-20 Konstantinos G. Lyras , Jack Lee