A SPECTRAL MULTIDOMAIN METHOD FOR THE NUMERICAL-SIMULATION OF TURBULENT FLOWS

The primitive variable formulation of the unsteady incompressible Navi er-Stokes equations in three space dimensions is discretized with a co mbined Fourier-Legendre spectral method. A semi-implicit pressure corr ection scheme is applied to decouple the velocity from the pressure. T he arising elliptic scaler problems are first diagonalized in the peri odic Fourier direction and then solved by a multidomain Legendre collo cation method in the two remaining space coordinates. In particular, b oth an iterative and a direct version of the so-called projection deco mposition method (PDM) are introduced to separate the equations for th e internal nodes from the ones governing the interface unknowns. The P DM method, first introduced by V. Agoshkov and E. Ovtchinnikov and lat er applied to spectral methods by P. Gervasio, E. Ovtchinnikov, and A. Quarteroni is a domain decomposition technique for elliptic boundary value problems, which is based on a Galerkin approximation of the Stek lov-Poincare equation for the unknown variables associated to the grid points lying on the interface between subdomains. After having shown the exponential convergence of the proposed discretization technique, some issues on the efficient implementation of the method are given. F inally, as an illustration of the potentialities of the algorithm for the numerical simulation of turbulent flows, the results of a direct n umerical simulation (DNS) of a fully turbulent plane channel flow are presented. (C) 1997 Academic Press.