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 error estimate for this weakly coupled two-level scheme are established. The proposed scheme is an effective algorithm since the non-linearity is treated only in the coarse-level subspace by solving the coarse level standard Galerkin equation and the matrix of the linear algebraic equations arising in each fine-level time stepping is a sparse matrix, especially for large scale computations. Therefore the new scheme saves a lot of CPU time and memory in comparison with the standard Fourier Galerkin method for deriving an approximation of prescribed accuracy. Oct 15, 2008, 4:00pm, Room:104 (Old Sciences Building)