Fourier-Chebyshev pseudospectral methods for the two-dimensional Navier-Stokes equations

Pseudospectral Solution of the Two-Dimensional Navier-Stokes Equations in a Disk

An efficient and accurate algorithm for solving the two-dimensional (2D) incompressible Navier–Stokes equations on a disk with no-slip boundary conditions is described. The vorticitystream function formulation of these equations is used, and spatially the vorticity and stream functions are expressed as Fourier–Chebyshev expansions. The Poisson and Helmholtz equations which arise from the implic...

Chebyshev spectral approximation of Navier-Stokes equations in a two dimensional domain

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Numerical Methods for the Navier-Stokes equations

Feedback Boundary Stabilization of the Two-Dimensional Navier--Stokes Equations

We study the exponential stabilization of the linearized Navier-Stokes equations around an unstable stationary solution, by means of a feedback boundary control, in dimension 2 or 3. The feedback law is determined by solving a Linear-Quadratic control problem. We do not assume that the normal component of the control is equal to zero. In that case the state equation, satisfied by the velocity f...

Postprocessing Fourier Galerkin Method for the Navier-Stokes Equations

A full discrete two-level postprocessing Fourier Galerkin scheme for the unsteady Navier-Stokes equations with periodic boundary conditions is proposed in this talk. By defining a new projection, the interaction between the large and small eddies is reflected by the associated space splitting to some extent. Then a weakly coupled system of the large and small eddies is obtained. Stability and e...