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A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is also…

Fluid Dynamics · Physics 2010-11-03 Helmut Abels , Harald Garcke , Günther Grün

We investigate experimentally the early stage of the generation of waves by a turbulent wind at the surface of a viscous liquid. The spatio-temporal structure of the surface deformation is analyzed by the optical method Free Surface…

Fluid Dynamics · Physics 2020-12-09 Anna Paquier , Frederic Moisy , Marc Rabaud

In this paper we propose a novel second-order accurate well balanced scheme for shallow water equations in general covariant coordinates over manifolds. In our approach, once the gravitational field is defined for the specific case, one…

Numerical Analysis · Mathematics 2022-12-08 Michele Giuliano Carlino , Elena Gaburro

We present a numerical method for interface-resolved simulations of evaporating two-fluid flows based on the volume-of-fluid (VoF) method. The method has been implemented in an efficient FFT-based two-fluid Navier-Stokes solver, using an…

Computational Physics · Physics 2020-01-24 Nicolò Scapin , Pedro Costa , Luca Brandt

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

Gravito-capillary waves at free-surfaces are ubiquitous in several natural and industrial processes involving quiescent liquid pools bounded by cylindrical walls. These waves emanate from the relaxation of initial interface distortions,…

Fluid Dynamics · Physics 2024-10-07 Lohit Kayal , Vatsal Sanjay , Nikhil Yewale , Anil Kumar , Ratul Dasgupta

An immersed-boundary method for the incompressible Navier--Stokes equations is presented. It employs discrete forcing for a sharp discrimination of the solid-fluid interface, and achieves second-order accuracy, demonstrated in examples with…

A new parallelized unsplit geometrical Volume of Fluid (VoF) algorithm with support for arbitrary unstructured meshes and dynamic local Adaptive Mesh Refinement (AMR), as well as for two and three dimensional computation is developed. The…

Fluid Dynamics · Physics 2013-05-16 Tomislav Maric , Holger Marschall , Dieter Bothe

In the present article we describe a few simple and efficient finite volume type schemes on moving grids in one spatial dimension combined with appropriate predictor-corrector method to achieve higher resolution. The underlying finite…

Numerical Analysis · Mathematics 2020-05-26 Gayaz Khakimzyanov , Denys Dutykh , Dimitrios Mitsotakis , Nina Shokina

We present an implicit-explicit finite volume scheme for isentropic two phase flow in all Mach number regimes. The underlying model belongs to the class of symmetric hyperbolic thermodynamically compatible models. The key element of the…

Numerical Analysis · Mathematics 2022-02-04 Maria Lukacova-Medvid'ova , Gabriella Puppo , Andrea Thomann

In this short note, we present an easy to implement and fast algorithm for the computation of the steady solitary gravity wave solution of the free surface Euler equations in irrotational motion. First, the problem is reformulated in a…

Fluid Dynamics · Physics 2020-02-20 Didier Clamond , Denys Dutykh

The performance of interFoam (a widely used solver within OpenFOAM package) in simulating the propagation of water waves has been reported to be sensitive to the temporal and spatial resolution. To facilitate more accurate simulations, a…

Fluid Dynamics · Physics 2020-10-15 Zhihang Zhang , Xizeng Zhao , Bin Xie

We are concerned with a model describing the motion of two compressible, immiscible fluids with density-dependent viscosity in the whole $\mathbb R^3$. The phases of the flow may have different pressure and viscosity laws and are separated…

Analysis of PDEs · Mathematics 2025-10-14 Marcel Zodji

The scattering of surface waves by structures intersecting liquid surfaces is fundamental in fluid mechanics, with prior studies exploring gravity, capillary, and capillary-gravity wave interactions. This paper develops a semi-analytical…

Fluid Dynamics · Physics 2026-01-21 Guoqin Liu , Likun Zhang

The present study focuses on the assessment of the performance of a Finite Volume Method based, particle-resolved simulation approach to predict the flow through a model packed-bed consisting of 21 layers of spheres arranged in the body…

This paper presents a general and robust method for the fluid-structure interaction of membranes and shells undergoing large displacement and large added-mass effects by coupling an immersed-boundary method with a shell finite-element…

Fluid Dynamics · Physics 2023-08-15 Marin Lauber , Gabriel D. Weymouth , Georges Limbert

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

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 propose a seamless multiscale method which approximates the macroscopic behavior of the passive advection-diffusion equations with steady incompressible velocity fields with multi-spatial scales. The method uses decompositions of the…

Numerical Analysis · Mathematics 2016-06-22 Yoonsang Lee , Bjorn Engquist

Accurate modeling of moving boundaries and interfaces is a difficulty present in many situations of computational mechanics. We use the eXtreme Mesh deformation approach (X-Mesh) to simulate the interaction between two immiscible flows…

Computational Engineering, Finance, and Science · Computer Science 2024-02-02 Antoine Quiriny , Jonathan Lambrechts , Nicolas Moës , Jean-François Remacle
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