Related papers: Mathematical model for coupling a quasi-unidimensi…
We consider the (complete) Euler system describing the motion of a compressible perfect fluid. We propose a platform suitable for constructing the statistical solutions. The main ingredients of our approach include: 1. The concept of…
We establish the global well-posedness of the free boundary problem of the viscous pressureless and almost pressureless heat conductive flows in one space dimension. In both cases, arbitrarily large but smooth initial data is considered,…
We study a generalization of the Navier-Stokes-Fourier system for an incompressible fluid where the deviatoric part of the Cauchy stress tensor is related to the symmetric part of the velocity gradient via a maximal monotone 2-graph that is…
In this paper, we present a novel approach to model the fluid/solid interaction forces in a direct solver of the Navier-Stokes equations based on the volume of fluid interface tracking method. The key ingredient of the model is the explicit…
This article is devoted to incompressible Euler equations (or to Navier-Stokes equations in the vanishing viscosity limit). It describes the propagation of quasi-singularities. The underlying phenomena are consistent with the notion of a…
The so-called 'direct' approach to separation of variables in linear PDEs is applied to the hydrodynamic stability problem. Calculations are made for the complete linear stability equations in cylindrical coordinates. Several classes of the…
We study the dynamics of the noncommutative fuid in the Snyder space perturbatively at the first order in powers of the noncommutative parameter. The linearized noncommutative fluid dynamics is described by a system of coupled linear…
A finite element model was developed to compute the fluid flow inside a sessile evaporating droplet on hydrophilic substrate in ambient conditions. The evaporation is assumed as quasi-steady and the flow is considered as axisymmetric with a…
This article introduces, and reviews recent work using, a simple optimisation technique for analysing the nonlinear stability of a state in a dynamical system. The technique can be used to identify the most efficient way to disturb a system…
We discuss the applicability of a unified hyperbolic model for continuum fluid and solid mechanics to modeling non-Newtonian flows and in particular to modeling the stress-driven solid-fluid transformations in flows of viscoplastic fluids,…
In this work, we discuss some points relevant for stochastic modelling of one- and two-phase turbulent flows. In the framework of stochastic modelling, also referred to PDF approach, we propose a new Langevin model including all viscosity…
We propose a kinetic framework for single-component non-ideal isothermal flows. Starting from a kinetic model for a non-ideal fluid, we show that under conventional scaling the Navier-Stokes equations with a non-ideal equation of state are…
The asymptotic derivation of a new family of one-dimensional, weakly nonlinear and weakly dispersive equations that model the flow of an ideal fluid in an elastic vessel is presented. Dissipative effects due to the viscous nature of the…
We study the existence and zero viscous limit of smooth solutions to steady compressible Navier-Stokes equations near plane shear flow between two moving parallel walls. Under the assumption $0<L\ll1$, we prove that for any plane supersonic…
A physical model of a three-dimensional flow of a viscous bubbly fluid in an intermediate regime between bubble formation and breakage is presented. The model is based on mechanics and thermodynamics of a single bubble coupled to the…
This paper investigates the global well-posedness and large-time behavior of solutions for a coupled fluid model in $\mathbb{R}^3$ consisting of the isothermal compressible Euler-Poisson system and incompressible Navier-Stokes equations…
The stability of idealized shear flow at long wavelengths is studied in detail. A hydrodynamic analysis at the level of the Navier-Stokes equation for small shear rates is given to identify the origin and universality of an instability at…
We report on two- and three-dimensional numerical simulations of Rayleigh-Taylor instabilities in immiscible fluids. A diffuse-interface model that combines the Cahn-Hilliard equation, governing the evolution of the volume fraction of one…
The viscous flow of two immiscible fluids in a porous medium on the Darcy scale is governed by a system of nonlinear parabolic equations. If infinite mobility of one phase can be assumed (e.g. in soil layers in contact with the atmosphere)…
Stationary adiabatic flows of real gases issued from a source of given intensity are studied. Thermodynamic states of gases are described by Legendrian or Lagrangian manifolds. Solutions of Euler equations are given implicitly for any…