We design an artificial boundary condition for the steady incompressible Navier-Stokes equations in streamfhction-vorticity formulation in a flat channel with slip boundary conditions on the wall. The new boundary condition is derived fiom the Oseen equations and the method of lines. A numerical experiment for the non-linear Navier-Stokes equations is presented. The artificial boundary conditio...

Droplet impact onto a solid surface is modeled and numerically simulated using an ALE formulation of the Navier-Stokes free surface equations. The triple line dynamics aspect is modeled implicitely through the Shikhmurzaev theory. Those equations involve a generalized Navier slip boundary conditions with the variation of the surface tension near the triple line (thus a local Marangoni effect). ...

Abstract. In this paper we prove a local exact controllability of the Navier–Stokes equations with the condition on the pressure on parts of the boundary. The local exact controllability is proved by using a global Carleman inequality and an estimate of an equation adjoint to a linearized Navier– Stokes equation with the nonstandard boundary condition. We also obtain the null controllability of...

We present a numerical simulation of two coupled Navier-Stokes flows, using operator-splitting and optimization-based nonoverlapping domain decomposition methods. The model problem consists of two Navier-Stokes fluids coupled, through a common interface, by a nonlinear transmission condition. Numerical experiments are carried out with two coupled fluids; one with an initial linear profile and t...

With the advent of microscale and nanoscale devices, the Navier-slip boundary condition as a macroscale model of fluid behaviour at a solid wall has seen renewed interest. The penalty concept and variational formulation are extended here to treat partial slip and related boundary conditions in viscous flow simulation. An analysis of the penalty partial-slip formulation permits us to relate it t...

Droplet impact onto a solid surface is modeled and numerically simulated using an ALE formulation of the Navier-Stokes free surface equations. The triple line dynamics aspect is modeled implicitely through the Shikhmurzaev theory. Those equations involve a generalized Navier slip boundary conditions with the variation of the surface tension near the triple line (thus a local Marangoni effect). ...

We consider the vanishing viscosity limit of the Navier-Stokes equations in a half space, with Dirichlet boundary conditions. We prove that the inviscid limit holds in the energy norm if the product of the components of the Navier-Stokes solutions are equicontinuous at x2 = 0. A sufficient condition for this to hold is that the tangential Navier-Stokes velocity remains uniformly bounded and has...

In this paper statistical solutions of the 3D Navier-Stokes-α model with periodic boundary condition are considered. It is proved that under certain natural conditions statistical solutions of the 3D Navier-Stokes-α model converge to statistical solutions of the exact 3D Navier-Stokes equations as α goes to zero. The statistical solutions considered here arise as families of time-projections of...

In a recent article the authors study the effect of replacing the standard no-slip boundary condition with a nonlinear Navier boundary condition for the boundary layer equations. The resulting equations contain an arbitrary index parameter, denoted by n, and it is found that the case n = 1 corresponding to linear Navier boundary condition must be excluded. In this article the authors remedy thi...