Related papers: Layer-averaged Euler and Navier-Stokes equations
In this paper, we first prove the global well-posedness of a scaled anisotropic Navier-Stokes system and the hydrostatic Navier-Stokes system in a 2-D striped domain with small analytic data in the tangential variable. Then we justify the…
In this work we present a multilayer shallow model to approximate the Navier-Stokes equations with hydrostatic pressure and the $\mu(I)$-rheology. The main advantages of this approximation are (i) the low cost associated with the numerical…
A numerical method, based on the discrete lattice Boltzmann equation, is presented for solving the volume-averaged Navier-Stokes equations. With a modified equilibrium distribution and an additional forcing term, the volume-averaged…
We develop a novel and efficient iterative scheme for solving incompressible steady Navier-Stokes equations. The method is an adaptation of the Incremental Viscosity Splitting approximation for unsteady flows to steady equations. At each…
In this paper, we present a new framework for the global well-posedness and large-time behavior of a two-phase flow system, which consists of the pressureless Euler equations and incompressible Navier-Stokes equations coupled through the…
In this paper we introduce (I,J) similar method for incompressible two and three dimensional Euler equations and Navier-Stokes equations, obtain a series of explicit (I,J) similar solutions to the incompressible two dimensional Euler…
In this work, we present a parametric finite element approximation of two-phase Navier-Stokes flow with viscoelasticity. The free boundary problem is given by the viscoelastic Navier-Stokes equations in the two fluid phases, connected by…
In this paper, the main objective is to generalize to the Navier-Stokes-Korteweg (with density dependent viscosities satisfying the BD relation) and Euler-Korteweg systems a recent relative entropy [proposed by D. Bresch, P. Noble and…
In this article, a suite of physically inconsistent properties of the Navier-Stokes equations, associated with the lack of mass diffusion and the definition of velocity, are presented. We show that these inconsistencies are consequences of…
In this paper, we study the hydrostatic approximation for the Navier-Stokes system in a thin domain. When the convex initial data with Gevrey regularity of optimal index 3/2 in x variable and Sobolev regularity in y variable, we justify the…
In this paper we propose a novel and general approach to design semi-implicit methods for the simulation of fluid-structure interaction problems in a fully Eulerian framework. In order to properly present the new method, we focus on the…
The paper introduces a geometrically unfitted finite element method for the numerical solution of the tangential Navier--Stokes equations posed on a passively evolving smooth closed surface embedded in $\mathbb{R}^3$. The discrete…
We consider the incompressible Euler or Navier-Stokes (NS) equations on a torus T^d in the functional setting of the Sobolev spaces H^n(T^d) of divergence free, zero mean vector fields on T^d, for n > d/2+1. We present a general theory of…
We provide an unconditional $L^2$ upper bound for the boundary layer separation of Leray-Hopf solutions in a smooth bounded domain. By layer separation, we mean the discrepancy between a (turbulent) low-viscosity Leray-Hopf solution $u^\nu$…
We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a domain in $\R^3$ with compact and smooth boundary, subject to the kinematic and Navier boundary conditions. We first reformulate the…
The aim of this paper is to show time-decay estimates of solutions to linearized two-phase Navier-Stokes equations with surface tension and gravity. The original two-phase Navier-Stokes equations describe the two-phase incompressible…
A well-established numerical approach to solve the Navier--Stokes equations for incompressible fluids is Chorin's projection method, whereby the fluid velocity is explicitly updated, and then an elliptic problem for the pressure is solved,…
We consider the two-phase dynamics of two incompressible and immiscible fluids. As a mathematical model we rely on the Navier-Stokes-Cahn-Hilliard system that belongs to the class of diffuse-interface models. Solutions of the…
Governing equations of motion for a viscous incompressible material surface are derived from the balance laws of continuum mechanics. The surface is treated as a time-dependent smooth orientable manifold of codimension one in an ambient…
This paper deals with the derivation of compressible two-phase flow models. We use a thin domain approximation of a two-layer configuration governed by the Navier-Stokes equations, following the works [H. B. Stewart and B. Wendroff, J.…