In this paper, we introduce a mixed finite element method on a staggered mesh for the numerical solution of the steady state Navier-Stokes equations in which the two components of the velocity and the pressure are defined on three different meshes. This method is a conforming quadrilateral Q1 × Q1 − P0 element approximation for the Navier-Stokes equations. First-order error estimates are obtain...

We present finite volume schemes for Stokes and Navier-Stokes equations. These schemes are based on the mixed finite volume introduced in [6], and can be applied to any type of grid (without “orthogonality” assumptions as for classical finite volume methods) and in any space dimension. We present numerical results on some irregular grids, and we prove, for both Stokes and Navier-Stokes equation...

This paper focuses on the notion of suitable weak solutions for the three-dimensional incompressible Navier–Stokes equations and discusses the relevance of this notion to Computational Fluid Dynamics. The purpose of the paper is twofold (i) to recall basic mathematical properties of the three-dimensional incompressible Navier-Stokes equations and to show how they relate to LES (ii) to introduce...

The numerical implementation of a multilevel finite element method for the steadystate Navier–Stokes equations is considered. The multilevel method proposed here for the Navier– Stokes equations is a multiscale method in which the full nonlinear Navier–Stokes equations are only solved on a single coarse grid; subsequent approximations are generated on a succession of refined grids by solving a ...

We study the weak boundary layer phenomenon of the Navier-Stokes equations with generalized Navier friction boundary conditions, u ·n = 0, [S(u)n] tan +Au = 0, in a bounded domain in R when the viscosity, ε > 0, is small. Here, S(u) is the symmetric gradient of the velocity, u, and A is a type (1, 1) tensor on the boundary. When A = αI we obtain Navier boundary conditions, and when A is the sha...

A multiscale method that couples direct simulation Monte Carlo (DSMC) method with Navier-Stokes equations is presented. The multiscale method is based on the Schwarz coupling of the DSMC and Navier-Stokes subdomains. Dirichlet boundary conditions are used at the coupling interfaces. The Navier-Stokes equations are solved using a scattered point based finite cloud method. Data interpolation betw...

This paper is based on a formulation of the Navier-Stokes equations developed by Iyer and Constantin \cite{Cont} , where velocity field viscous incompressible fluid written as expected value stochastic process. Our contribution to establish this probabilistic representation formula for mild solutions $\mathbb{R}^{d} $.

The motion of a viscous incompressible fluid flow in bounded domains with a smooth boundary can be described by the nonlinear Navier-Stokes equations. This description corresponds to the so-called Eulerian approach. We develop a new approximation method for the Navier-Stokes equations in both the stationary and the non-stationary case by a suitable coupling of the Eulerian and the Lagrangian re...