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This paper studies a model of two-phase flow with an immersed material viscous interface and a finite element method for numerical solution of the resulting system of PDEs. The interaction between the bulk and surface media is characterized…
We propose a simple modification of standard WENO finite volume methods for Cartesian grids, which retains the full spatial order of accuracy of the one-dimensional discretization when applied to nonlinear multidimensional systems of…
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.…
In this article, we present a cut finite element method for two-phase Navier-Stokes flows. The main feature of the method is the formulation of a unified continuous interior penalty stabilisation approach for, on the one hand, stabilising…
In multiphase flow phenomena, bubbles and droplets are advected, deformed, break up into smaller ones, and coalesce with each other. A primary challenge of classical computational fluid dynamics (CFD) methods for such flows is to…
In this paper, we consider a non-local (in time) two-phase flow model. The non-locality is introduced through the wettability alteration induced dynamic capillary pressure function. We present a monotone fixed-point iterative linearization…
We implement the level set method for numerical simulation of the motion of a suspended particle convected by the fluid flow in a microchannel. The method automatically cope with the interactions between the particle and the channel walls.…
As model problem we consider the prototype for flow and transport of a concentration in porous media in an interior domain and couple it with a diffusion process in the corresponding unbounded exterior domain. To solve the problem we…
This paper presents a method for modelling interfacial mass transfer in Interface Capturing simulations of two-phase flow with phase change. The model enables mechanistic prediction of the local rate of phase change at the vapour-liquid…
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…
In this paper, we present an efficient numerical algorithm for solving the time-dependent Cahn--Hilliard--Navier--Stokes equations that model the flow of two phases with different densities. The pressure-correction step in the projection…
We study a one dimensional model for two-phase flows in heterogeneous media, in which the capillary pressure functions can be discontinuous with respect to space. We first give a model, leading to a system of degenerated non-linear…
We introduce a new Eulerian simulation framework for liquid animation that leverages both finite element and finite volume methods. In contrast to previous methods where the whole simulation domain is discretized either using the finite…
We present a novel immersed boundary method that implements acoustic perturbation theory to model an acoustically levitated droplet. Instead of resolving sound waves numerically, our hybrid method solves acoustic scattering…
We introduce a second-order numerical scheme for compressible atmospheric motions at small to planetary scales. The collocated finite volume method treats the advection of mass, momentum, and mass-weighted potential temperature in…
Modeling of a dense spray regime using an Euler-Lagrange approach is challenging because of local high volume loading. A cluster of droplets, that are assumed subgrid, can lead to locally low void fractions for the fluid phase. Under these…
We propose and analyze unfitted finite element approximations for the two-phase incompressible Navier--Stokes flow in an axisymmetric setting. The discretized schemes are based on an Eulerian weak formulation for the Navier--Stokes equation…
A low-Mach-number flow, in the laminar regime, has intrinsically two characteristic spatial scales for a given time scale, or two characteristic temporal scales for a given spatial scale, and these dual scales are very different due to the…
In this article, we propose a novel scalar-transport model for the simulation of scalar quantities in two-phase flows with a phase-field method (diffuse-interface method). In a two-phase flow, the scalar quantities typically have disparate…
In this fluid dynamics video, results from high fidelity numerical simulations are presented, which have been carried out to study the flow and droplet dynamics of liquid sheets formed by two impinging jets. A three-dimensional…