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A thermodynamically consistent two-phase Stefan problem with temperature-dependent surface tension and with or without kinetic undercooling is studied. It is shown that these problems generate local semiflows in well-defined state…

Analysis of PDEs · Mathematics 2016-12-20 Jan Pruess , Gieri Simonett , Mathias Wilke

In this paper, for the first time we propose two linear, decoupled, energy-stable numerical schemes for multi-component two-phase compressible flow with a realistic equation of state (e.g. Peng-Robinson equation of state). The methods are…

Numerical Analysis · Mathematics 2017-12-12 Jisheng Kou , Shuyu Sun , Xiuhua Wang

We present an hybrid VOF/embedded boundary method allowing to model two-phase flows in presence of solids with arbitrary shapes. The method relies on the coupling of existing methods: a geometric Volume of fluid (VOF) method to tackle the…

Analyzing complex fluid flow problems that involve multiple coupled domains, each with their respective set of governing equations, is not a trivial undertaking. Even more complicated is the elaborate and tedious task of specifying the…

Fluid Dynamics · Physics 2017-08-18 Alexandre Martin , Huaibao Zhang , Kaveh A. Tagavi

We introduce a new sharp interface model for the flow of two immiscible, viscous, incompressible fluids. In contrast to classical models for two-phase flows we prescribe an evolution law for the interfaces that takes diffusional effects…

Analysis of PDEs · Mathematics 2015-05-13 Helmut Abels , Matthias Röger

We present a parametric finite element approximation of two-phase flow. This free boundary problem is given by the Navier--Stokes equations in the two phases, which are coupled via jump conditions across the interface. Using a novel…

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

Simple observations of evaporating solutions reveal a complex hierarchy of spatio-temporal instabilities. We analyze one such instability suggested by the qualitative observations of Du and Stone and find that it is driven by a novel…

Statistical Mechanics · Physics 2012-01-17 Robert W. Style , John. S. Wettlaufer

This paper presents results for the sampled-data boundary feedback control to the Stefan problem. The Stefan problem represents a liquid-solid phase change phenomenon which describes the time evolution of a material's temperature profile…

Optimization and Control · Mathematics 2019-06-05 Shumon Koga , Iasson Karafyllis , Miroslav Krstic

We study an interface-capturing two-phase fluid model in which the interfacial tension is modelled as a volumetric stress. Since these stresses are obtainable from a Van der Waals-Cahn-Hilliard free energy, the model is, to a certain…

comp-gas · Physics 2008-02-03 B. T. Nadiga , S. Zaleski

We consider steady solutions to the incompressible Euler equations in a two-dimensional channel with rigid walls. The flow consists of two periodic layers of constant vorticity separated by an unknown interface. Using global bifurcation…

Analysis of PDEs · Mathematics 2025-06-23 Alex Doak , Karsten Matthies , Jonathan Sewell , Miles H. Wheeler

We analyze a diffuse interface model for multi-phase flows of $N$ incompressible, viscous Newtonian fluids with different densities. In the case of a bounded and sufficiently smooth domain existence of weak solutions in two and three space…

Analysis of PDEs · Mathematics 2024-01-15 Helmut Abels , Harald Garcke , Andrea Poiatti

We study a moisture model for warm clouds that has been used by Klein and Majda as a basis for multiscale asymptotic expansions for deep convective phenomena. These moisture balance equations correspond to a bulk microphysics closure in the…

Analysis of PDEs · Mathematics 2017-10-11 Sabine Hittmeir , Rupert Klein , Jinkai Li , Edriss S. Titi

We consider a coupled two-phase Navier-Stokes/Mullins-Sekerka system describing the motion of two immiscible, incompressible fluids inside a bounded container. The moving interface separating the liquids meets the boundary of the container…

Analysis of PDEs · Mathematics 2020-02-04 Maximilian Rauchecker , Mathias Wilke

The injection of liquid fuel at supercritical pressures is a relevant topic in combustion, but usually overlooked. In the past, the wrong assumption whereby the liquid experiments a fast transition to a supercritical state was made, thus…

Fluid Dynamics · Physics 2021-12-14 Jordi Poblador-Ibanez , William A. Sirignano

We study single-interface solutions to a free boundary problem that couples bilinear bulk diffusion to the Stefan condition and a hysteretic flow rule for phase boundaries. We introduce a time-discrete approximation scheme and establish its…

Analysis of PDEs · Mathematics 2024-04-23 Michael Herrmann , Dirk Janßen

We investigate a diffuse-interface model that describes the dynamics of incompressible two-phase viscous flows with surfactant. The resulting system of partial differential equations consists of a sixth-order Cahn-Hilliard equation for the…

Analysis of PDEs · Mathematics 2023-07-28 Andrea Di Primio , Maurizio Grasselli , Hao Wu

We propose a model that describes phase transition including meta\-stable states present in the van der Waals Equation of State. From a convex optimization problem on the Helmoltz free energy of a mixture, we deduce a dynamical system that…

Statistical Mechanics · Physics 2016-03-15 Francois James , Hélène Mathis

The stability of the interface separating two immiscible incompressible fluids of different densities and viscosities is considered in the case of fluids filling a cavity which performs horizontal harmonic oscillation. There exists a simple…

Fluid Dynamics · Physics 2009-10-31 Mikhail V. Khenner , Dmitrii V. Lyubimov , Tatyana S. Belozerova , Bernard Roux

A general diffuse interface model with a realistic equation of state (e.g. Peng-Robinson equation of state) is proposed to describe the multi-component two-phase fluid flow based on the principles of the NVT-based framework which is a…

Numerical Analysis · Mathematics 2016-11-29 Jisheng Kou , Shuyu Sun

We perform high-order simulations of two-phase flows in capillaries, with and without evaporation. Since a sharp-interface model is used, singularities can arise at the three-phase contact line, where the fluid-fluid interface interacts…

Fluid Dynamics · Physics 2025-02-14 Irina Shishkina , Matthias Rieckmann , Martin Oberlack , Florian Kummer