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 a periodic boundary condition is proposed in this paper. By defining a new projection, the interaction between the large and small eddies is reflected by the associated space splitting to some extent. Therefore, a weakly coupled system of the large and small eddies is obtained. Stability and error estimates for the weakly coupled two-level scheme are established in the paper. The proposed scheme is an effective algorithm because nonlinearity 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. As a result, 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. [ABSTRACT FROM AUTHOR]