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Conventional mathematical models for simulating incompressible fluid flow problems are based on the Navier-Stokes equations expressed in terms of pressure and velocity. In this context, pressure-velocity coupling is a key issue, and…

Mathematical Physics · Physics 2025-06-06 Ricardo Costa , Stéphane Clain , Gaspar J. Machado , João M. Nóbrega

We present a computational framework to address the flow of two immiscible viscous liquids which co-flow into a shallow rectangular container at one side, and flow out into a holding container at the opposite side. Assumptions based on the…

Fluid Dynamics · Physics 2013-09-02 Shahriar Afkhami , Yuriko Renardy

We present a novel framework to deal with static and moving immersed boundaries (IB). In this strategy, called Volume-Filtering Immersed Boundary (VFIB) method, transport equations are derived by filtering the Navier-Stokes equations and…

Fluid Dynamics · Physics 2023-05-24 Himanshu Dave , Marcus Herrmann , M. Houssem Kasbaoui

We consider the numerical approximation of a sharp-interface model for two-phase flow, which is given by the incompressible Navier-Stokes equations in the bulk domain together with the classical interface conditions on the interface. We…

Numerical Analysis · Mathematics 2023-06-21 Harald Garcke , Robert Nürnberg , Quan Zhao

Vocal fold (VF) motion is a fundamental process in voice production, and is also a challenging problem for direct numerical computation because the VF dynamics depend on nonlinear coupling of air flow with the response of elastic channels…

Pattern Formation and Solitons · Physics 2009-11-07 M. Drew LaMar , Yingyong Qi , Jack Xin

Surfactants reside at the interface of two-phase flows and significantly influence the flow dynamics. Numerical simulations are essential for a comprehensive understanding of such surfactant-laden flows and require a method that can…

Fluid Dynamics · Physics 2026-05-20 Shu Yamashita , Shintaro Matsushita , Tetsuya Suekane

The numerical simulation of wetting and dewetting of geometrically complex surfaces benefits from unstructured numerical methods because they discretize the domain with second-order accuracy. A recently developed unstructured geometric…

Fluid Dynamics · Physics 2025-01-08 Muhammad Hassan Asghar , Mathis Fricke , Dieter Bothe , Tomislav Maric

Two new control volume solvers multiFluidInterFoam and rheoMultiFluidInterFoam are presented for the simulation of Newtonian and non-Newtonian n-phase flows, respectively, fully accounting for interfacial tension and contact-angle effects…

Fluid Dynamics · Physics 2022-03-21 Chris Dritselis , George Karapetsas

We propose an efficient numerical method for the simulation of multi-phase flows with moving contact lines in three dimensions. The mathematical model consists of the incompressible Navier-Stokes equations for the two immiscible fluids with…

Fluid Dynamics · Physics 2023-02-08 Quan Zhao , Shixin Xu , Weiqing Ren

A new PLIC (piecewise linear interface calculation)-type VOF (volume of fluid) method, called APPLIC (approximated PLIC) method, is presented. Although the PLIC method is one of the most accurate VOF methods, the three-dimensional algorithm…

Computational Physics · Physics 2016-05-27 Akio Kawano

Classical continuum-based liquid vapour phase-change models typically assume continuity of temperature at phase interfaces along with a relation which describes the rate of evaporation at the interface (Hertz-Knudsen-Schrage, for example).…

Fluid Dynamics · Physics 2021-06-10 Anirudh S Rana , Sonu Saini , Suman Chakraborty , Duncan A Lockerby , James E Sprittles

Surfactant transport plays an important role in many technical processes and industrial applications such as chemical reactors, microfluidics, printing and coating technology. High fidelity numerical simulations of two-phase flow phenomena…

Fluid Dynamics · Physics 2023-11-16 T. Antritter , T. Josyula , T. Marić , D. Bothe , P. Hachmann , B. Buck , T. Gambaryan-Roisman , P. Stephan

In this paper, we investigate numerically a diffuse interface model for the Navier-Stokes equation with fluid-fluid interface when the fluids have different densities \cite{Lowengrub1998}. Under minor reformulation of the system, we show…

Mathematical Physics · Physics 2015-06-18 Zhenlin Guo , Ping Lin , John S. Lowengrub

One of the prevailing challenges in Computational Fluid Dynamics is accurate simulation of two-phase flows involving heat and mass transfer across the fluid interface. This is currently an active field of research, which is to some extend…

Fluid Dynamics · Physics 2021-03-02 Henning Scheufler , Johan Roenby

Long liquid retention times in industrial gaps, due to capillary effects, significantly affect product lifetime by facilitating corrosion on solid surfaces. Concentration-driven evaporation plays a major role in mitigating this corrosion.…

Fluid Dynamics · Physics 2025-05-20 Phil Namesnik , Alexander Eifert , Anja Lippert , Louis Mett , Uwe Janoske

The gVOF package includes a complete and self-contained set of routines for volume of fluid initialization, interface reconstruction and fluid advection, which are used to implement several accurate and efficient geometric volume of fluid…

Computational Physics · Physics 2022-05-25 Joaquín López , Julio Hernández

This study presents a novel pressure-based methodology for the efficient numerical solution of a four-equation two-phase diffuse interface model. The proposed methodology has the potential to simulate low-Mach flows with mass transfer. In…

Fluid Dynamics · Physics 2021-10-12 Andreas D. Demou , Nicoló Scapin , Marica Pelanti , Luca Brandt

In this work, we propose a novel phase-field model for the simulation of two-phase flows that is accurate, conservative, bounded, and robust. The proposed model conserves the mass of each of the phases, and results in bounded transport of…

Computational Physics · Physics 2022-08-23 Suhas S. Jain

The capillary time-step constraint is the dominant limitation on the applicable time-step in many simulations of interfacial flows with surface tension and, consequently, governs the execution time of these simulations. We propose a…

Computational Physics · Physics 2022-03-10 Fabian Denner , Fabien Evrard , Berend van Wachem

This work describes three diffuse-interface methods for the simulation of immiscible, compressible multiphase fluid flows and elastic-plastic deformation in solids. The first method is the localized-artificial-diffusivity approach of Cook…

Computational Physics · Physics 2021-09-21 Suhas S. Jain , Michael C. Adler , Jacob R. West , Ali Mani , Parviz Moin , Sanjiva K. Lele