The MAC discretization scheme for the incompressible NavierStokes equations is interpreted as a covolume approximation to the equations. Using some results from earlier papers dealing with covolume error estimates for div-curl equation systems, and under certain conditions on the data and the solutions of the Navier-Stokes equations, we obtain first-order error estimates for both the vorticity ...

A computational study was conducted to investigate the unsteady quasi-two-dimensional flow around a streamlined NASA low-speed GA(W)-1 airfoil and a corrugated dragonfly airfoil at the Reynolds numbers of 68,000 and 55,000. Both 2D and 3D simulations were carried out by solving the unsteady Navier-Stokes equations to predict the behavior of the unsteady flow structures around the airfoils at di...

Molecule spaces have been introduced by Furioli and Terraneo [Funkcial. Ekvac., 45 (2002), pp. 141–160] to study some local behavior of solutions to the Navier–Stokes equations. In this paper we give a new characterization of these spaces and simplify Furioli and Terraneo’s result. Our analysis also provides a persistence result for Navier–Stokes in a subspace of L2(R3, (1 + |x|2)αdx), α < 5/2,...

This paper considers the flow in a two-dimensional channel at high Reynolds number, with wall deformationswhich can lead to flow separation. An asymptoticmodel is proposed by using the successive complementary expansion method with generalized asymptotic expansions. In particular, the model emphasizes the asymmetry of the channel geometry by introducing a change of variables. It is shown that t...

1. Introduction. In this note we will study a special class of solutions of the three-dimensional steady-state Navier-Stokes equations

While biological flyers often display deformed wing structures, the effects of flexibility on the flapping wing aerodynamics remain inadequately understood. We investigate the lift generation and phase dynamics of a flapping flexible wing in hover, between Reynolds number of 100 and 1000 corresponding to small insects, using fully coupled Navier-Stokes equation and linear beam model. The γ scal...

We prove that any weak space-time L vanishing viscosity limit of a sequence of strong solutions of Navier-Stokes equations in a bounded domain of R satisfies the Euler equation if the solutions’ local enstrophies are uniformly bounded. We also prove that t − a.e. weak L inviscid limits of solutions of 3D Navier-Stokes equations in bounded domains are weak solutions of the Euler equation if they...

On compactness of solutions to the compressible isentropic Navier-Stokes equations when the density is not square integrable Abstract. We show compactness of bounded sets of weak solutions to the isentropic compressible Navier-Stokes equations in three space dimensions under the hypothesis that the adiabatic constant γ > 3/2.

Numerical solvers of the incompressible Navier-Stokes equations have reproduced turbulence phenomena such as the law of the wall, the dependence of turbulence intensities on the Reynolds number, and experimentally observed properties of turbulence energy production. In this article, we begin a sequence of investigations whose eventual aim is to derive and implement numerical solvers that can re...

This paper presents mathematical properties of solutions to the Navier-Stokes equations for compressible fluids. We first review existence results for the Cauchy problem, and describe some regularity properties of solutions in the presence of possibly vanishing densities. Finally, we address the problem of the low Mach number limit leading to incompressible models.