in this paper, optimal distributed control of the time-dependent navier-stokes equations is considered. the control problem involves the minimization of a measure of the distance between the velocity field and a given target velocity field. a mixed numerical method involving a quasi-newton algorithm, a novel calculation of the gradients and an inhomogeneous navier-stokes solver, to find the opt...

In this paper, optimal distributed control of the time-dependent Navier-Stokes equations is considered. The control problem involves the minimization of a measure of the distance between the velocity field and a given target velocity field. A mixed numerical method involving a quasi-Newton algorithm, a novel calculation of the gradients and an inhomogeneous Navier-Stokes solver, to find the opt...

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 study the relations between the long-time dynamics of the Navier–Stokes-α model and the exact 3D Navier–Stokes system. We prove that bounded sets of solutions of the Navier–Stokes-α model converge to the trajectory attractor A0 of the 3D Navier–Stokes system as time tends to infinity and α approaches zero. In particular, we show that the trajectory attractor Aα of the Navier–Stokes-α model c...

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 deal with the local exact controllability of the Navier-Stokes system with nonlinear Navier-slip boundary conditions and distributed controls supported in small sets. In a first step, we prove a Carleman inequality for the linearized Navier-Stokes system, which leads to null controllability of this system at any time T > 0. Then, fixed point arguments lead to the dedu...

We consider dynamics system with damping, which are obtained by some transformations from the system of incompressible Navier-Stokes equations. These have similar properties to original Navier-Stokes equations the scaling invariance. Due to the presence of the damping term, conclusions are different with proving the origin of the incompressible Navier-Stokes equations and get some new conclusio...

The application of Krylov subspace iterative methods to unsteady three-dimensional Navier–Stokes codes on massively parallel and distributed computing environments is investigated. Previously, the Euler mode of the Navier–Stokes flow solver Transonic Unsteady Rotor Navier–Stokes (TURNS) has been coupled with a Newton–Krylov scheme which uses two Conjugate-Gradient-like (CG) iterative methods. F...

We study the asymptotic behavior, at small viscosity ε, of the NavierStokes equations in a 2D curved domain. The Navier-Stokes equations are supplemented with the slip boundary condition, which is a special case of the Navier friction boundary condition where the friction coefficient is equal to two times the curvature on the boundary. We construct an artificial function, which is called a corr...

The aim of this paper is to introduce and validate a coupled Navier-Stokes Boltzmann approach for the calculation of hypersonic rareeed ows around manoeuver-ing vehicles. The proposed strategy uses locally a kinetic model in the boundary layer coupled through wall friction forces to a global Navier-Stokes solver. Diierent numerical experiments illustrate the potentialities of the method. Coupla...