Numerical study on comparison of Navier-Stokes and Burgers equations

A comparative study between two numerical solutions of the Navier-Stokes equations

The present study aimed to investigate two numerical solutions of the Navier-Stokes equations. For this purpose, the mentioned flow equations were written in two different formulations, namely (i) velocity-pressure and (ii) vorticity-stream function formulations. Solution algorithms and boundary conditions were presented for both formulations and the efficiency of each formulation was investiga...

Exponential Ergodicity for Stochastic Burgers and 2d Navier-stokes Equations

It is shown that transition measures of the stochastic Navier-Stokes equation in 2D converge exponentially fast to the corresponding invariant measures in the distance of total variation. As a corollary we obtain the existence of spectral gap for a related semigroup obtained by a sort of ground state trasformation. Analogous results are proved for the stochastic Burgers equation.

Numerical Methods for the Navier-Stokes equations

On the Numerical Controllability of the Two-Dimensional Heat, Stokes and Navier-Stokes Equations

The aim of this work is to present some strategies to solve numerically controllability problems for the two-dimensional heat equation, the Stokes equations and the Navier-Stokes equations with Dirichlet boundary conditions. The main idea is to adapt the Fursikov-Imanuvilov formulation, see [A.V. Fursikov, O.Yu. Imanuvilov: Controllability of Evolutions Equations, Lectures Notes Series, Vol. 34...

Optimization with the time-dependent Navier-Stokes equations as constraints

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...