We present in this paper a rigorous error analysis of certain projection schemes for the approximation of the unsteady incompressible Navier-Stokes equations. The error analysis is accomplished by interpreting the respective projection schemes as second-order time discretizations of a perturbed system which approximates the Navier-Stokes equations. Numerical results in agreement with the error ...

We introduce a dyadic model for the Euler equations and the Navier-Stokes equations with hyper-dissipation in three dimensions. For the dyadic Euler equations we prove finite time blow-up. In the context of the dyadic Navier-Stokes equations with hyper-dissipation we prove finite time blow-up in the case when the dissipation degree is sufficiently small.

This paper continues the development of the least-squares methodology for the solution of the incompressible Navier-Stokes equations started in Part I. Here we again use a velocityflux first-order Navier-Stokes system, but our focus now is on a practical algorithm based on a discrete negative norm.

We study spatial analyticity properties of solutions of the Navier-Stokes equation and obtain new growth rate estimates for the analyticity radius. We also study stability properties of strong global solutions of the Navier-Stokes equation with data in H, r ≥ 1/2 and prove a stability result for the analyticity radius.

We obtain a pointwise, a priori bound for the vorticity of axis symmetric solutions to the 3 dimensional Navier-Stokes equations. The bound is in the form of a reciprocal of a power of the distance to the axis of symmetry. This seems to be the first general pointwise estimate established for the axis symmetric Navier-Stokes equations.

In this paper we establish the local exact internal controllability of steady state solutions for the Navier-Stokes equations in three-dimensional bounded domains, with the Navier slip boundary conditions. The proof is based on a Carlemantype estimate for the backward Stokes equations with the same boundary conditions, which is also established here.

In the last decade or so, the lattice Boltzmann (LB) method has emerged as a new and effective numerical technique of computational fluid dynamics (CFD).(1-5) Modeling of the incompressible Navier-Stokes equation is among many of its wide applications. Indeed, the lattice Boltzmann equation (LBE) was first proposed to simulate the incompressible NavierStokes equations.(1) The incompressible Nav...

In this paper we show how Scilab can be used to solve Navier-stokes equations, for the incompressible and stationary planar flow. Three examples have been presented and some comparisons with reference solutions are provided. Contacts [email protected] This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. Navier-Stokes finite element sol...

We report on recent progress towards the development of a 3D optimization capability for transonic ow at high Reynolds numbers. In this paper we demonstrate optimization based on the 3D laminar Navier-Stokes equation, and we present validation of the ow analysis scheme based on the 2D Navier-Stokes equations with turbulence modelling.

We consider a hyperbolicly perturbed Navier-Stokes initial value problem in R, n = 2, 3, arising from using a Cattaneo type relation instead of a Fourier type one in the constitutive equations. The resulting system is a hyperbolic one with quasilinear nonlinearities. The global existence of smooth solutions for small data is proved, and relations to the classical Navier-Stokes systems are discu...