 
Summary: MULTIDIMENSIONAL PARALLEL SPECTRAL SOLVER
FOR NAVIERSTOKES EQUATIONS
AMIR AVERBUCH \Lambda , LUDIMILA IOFFE y , MOSHE ISRAELI y , AND
LEV VOZOVOI \Lambda
Abstract. In this paper we present a survey and new parallel algorithms for the
solution of the incompressible two and threedimensional NavierStokes equations. We
present a highorder parallel algorithms which require only minimum interprocessor
communication which is dictated by the physical nature of the problem at hand. The
parallelization is achieved via domain decomposition. We consider computational regions
in the form of a 2D or 3D periodic box which is decomposed into parallel strips (slabs)
and cells. The time discretization is performed via the semiimplicit splitting scheme
of [33]. The splitting procedure in time results in solving in each time step two global
elliptic equations: the Poisson equation for the determination of the pressure field and
the Helmholtz equation for the implicit viscous step. The discretization in space is
performed using the Local Fourier Basis method [23] and the multidomain local Fourier
(MDLF) method that was developed in [13, 79, 12, 13, 29, 30, 37, 40]. Therefore, in
the direction across the strip or cells we use the Local Fourier Basis technique which
involves the overlapping of the neighboring subdomains and smoothing of local functions
across the interior boundaries (interfaces). The discretization in the periodic directions
is performed by the standard Fourier method. To avoid the Gibbs phenomenon, the
