come several intrinsic limitations of spectral methods, allowing for the use of the latter in a wider context .
The primitive variable formulation of the unsteady incompressible Navier-Stokes equations in three space dimensions is discretized The most obvious application of spectral multidomain with a combined Fourier-Legendre spectral method. A semi-implicit methods is related to the solution of partial differential pressure correction scheme is applied to decouple the velocity from equations over complex geometries (i.e., geometries which the pressure. The arising elliptic scalar problems are first diagonalcannot be trivially mapped in the standard [Οͺ1, 1] square).
ized in the periodic Fourier direction and then solved by a multido-Another important feature of this class of algorithms is main Legendre collocation method in the two remaining space coordinates. In particular, both an iterative and a direct version of the the natural way in which they exploit the architectures of so-called projection decomposition method (PDM) are introduced modern MIMD computers (including clusters of workto separate the equations for the internal nodes from the ones stations) paving the way for large scale simulations othergoverning the interface unknowns. The PDM method, first introwise accessible only to supercomputer users. In fact, the duced by V. Agoshkov and E. Ovtchinnikov and later applied to spectral methods by P. Gervasio, E. Ovtchinnikov, and A. Quarteroni parallelization efficiency is extremely favourable to specis a domain decomposition technique for elliptic boundary value tral multidomain methods: the ratio of computation time problems, which is based on a Galerkin approximation of the to communication time is larger for this family of methods Steklov-Poincare Β΄equation for the unknown variables associated to than for others. This is mainly due to the high order accuthe grid points lying on the interface between subdomains. After racy provided by the spectral method combined with the having shown the exponential convergence of the proposed discretization technique, some issues on the efficient implementation of fact that the discrete operators involve matrices not as the method are given. Finally, as an illustration of the potentialities sparse as other ''local'' methods (i.e., finite differences, of the algorithm for the numerical simulation of turbulent flows, finite element or finite volumes) .
the results of a direct numerical simulation (DNS) of a fully turbulent
The present Navier-Stokes solution algorithm differs plane channel flow are presented.