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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

The finite volume methods are frequently employed in the discretization of diffusion problems with interface. In this paper, we firstly present a vertex-centered MACH-like finite volume method for solving stationary diffusion problems with…

Numerical Analysis · Mathematics 2016-09-07 Jie Peng , Shi Shu , Haiyuan Yu , Chunsheng Feng , Mingxian Kan , Ganghua Wang

We study convergence of a finite volume scheme for the Navier-Stokes-Fourier system describing the motion of compressible viscous and heat conducting fluids. The numerical flux uses upwinding with an additional numerical diffusion of order…

Numerical Analysis · Mathematics 2019-03-21 Eduard Feireisl , Maria Lukacova-Medvidova , Hana Mizerova , Bangwei She

We propose a finite volume scheme for computing two-fluid flows in variable cross-section ducts. Our scheme satisfies a well-balanced property. It is based on the VFRoe approach. The VFRoe variables are the Riemann invariants of the…

Analysis of PDEs · Mathematics 2014-03-07 Philippe Helluy , Jonathan Jung

Liquid-liquid wetting failure is investigated in a two-dimensional Couette system with two immiscible fluids of arbitrary viscosity. The problem is solved exactly using a sharp interface treatment of hydrodynamics (lubrication theory) as a…

Fluid Dynamics · Physics 2009-11-13 M. Sbragaglia , K. Sugiyama , L. Biferale

We consider a two-phase problem for two incompressible, viscous and immiscible fluids which are separated by a sharp interface. The problem arises as a sharp interface limit of a diffuse interface model. We present results on local…

Analysis of PDEs · Mathematics 2012-09-17 Helmut Abels , Mathias Wilke

In this work we define a mean-field crossover generated by the Maxwell construction as the dividing interface for the vapor-liquid interface area. A highly accurate density-profile equation is thus derived, which is physically favorable and…

Soft Condensed Matter · Physics 2021-10-18 Hongqin Liu

We adapt and extend a formulation for soluble surfactant transport in multiphase flows recently presented by Muradoglu & Tryggvason (JCP 274 (2014) 737-757) to the context of the Level Contour Reconstruction Method (Shin et al. IJNMF 60…

Computational Engineering, Finance, and Science · Computer Science 2018-03-14 Seungwon Shin , Jalel Chergui , Damir Juric , Lyes Kahouadji , Omar K. Matar , Richard V. Craster

We consider the simulation of barotropic flow of gas in long pipes and pipe networks. Based on a Hamiltonian reformulation of the governing system, a fully discrete approximation scheme is proposed using mixed finite elements in space and…

Numerical Analysis · Mathematics 2023-03-01 H. Egger , J. Giesselmann , T. Kunkel , N. Philippi

A variational volume-of-fluid (VVOF) methodology is devised for evolving interfaces under curvature-dependent speed. The interface is reconstructed geometrically using the analytic relations of Scardovelli and Zaleski [1] and the advection…

Numerical Analysis · Mathematics 2023-03-29 Ali Fakhreddine , Karim Alamé , Krishnan Mahesh

An existing phase-field model of two immiscible fluids with a single soluble surfactant present is discussed in detail. We analyze the well-posedness of the model and provide strong evidence that it is mathematically ill-posed for a large…

Numerical Analysis · Mathematics 2013-03-20 Stefan Engblom , Minh Do-Quang , Gustav Amberg , Anna-Karin Tornberg

We propose finite-volume schemes for the Cahn-Hilliard equation which unconditionally and discretely preserve the boundedness of the phase field and the dissipation of the free energy. Our numerical framework is applicable to a variety of…

Numerical Analysis · Mathematics 2023-12-18 Rafael Bailo , José A. Carrillo , Serafim Kalliadasis , Sergio P. Perez

In this work, we propose a novel transport model for soluble surfactants in two-phase flows. In a two-phase flow, the soluble surfactants can adsorb/desorb from/into the bulk of any of the phases to the interface and can modify the…

Fluid Dynamics · Physics 2025-10-14 Suhas S. Jain

Instead of ensuring that fluxes across edges add up to zero, we split the edge in two halves and also associate different fluxes to each of its sides. This is possible due to non-standard Riemann solvers with free parameters. We then…

Numerical Analysis · Mathematics 2024-08-27 Wasilij Barsukow , Raphaël Loubère , Pierre-Henri Maire

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

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 present a parametric finite element approximation of two-phase flow with insoluble surfactant. This free boundary problem is given by the Navier--Stokes equations for the two-phase flow in the bulk, which are coupled to the transport…

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

Developing high-order numerical schemes for two-phase flow in porous media that preserve key physical properties remains a significant challenge in numerical analysis. In this article, we propose a general framework to construct fully…

Numerical Analysis · Mathematics 2026-05-29 Xiaoli Li , Cheng Wang , Yujing Yan , Nan Zheng

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

This paper proposes a diffuse-interface model for simulating gas-liquid-solid multiphase flows involving solid-liquid phase change, solute transport, and the Marangoni effect. In this model, a phase-field method is employed to capture the…

Fluid Dynamics · Physics 2025-11-13 Jiangxu Huang , Zhenhua Chai , Xi Liu , Changsheng Huang