D ϭ 3.1. The drag history, shown in (c), agrees well with the results of [24] which were based upon an adaptive Efficient solution of the Navier-Stokes equations in complex domains is dependent upon the availability of fast solvers for sparse vortex method using up to 10 6 elements. The present calculinear systems. For unsteady incompressible flows, the pressure lation used a total of K ϭ 6112 spectral elements, with the operator is the leading contributor to stiffness, as the characteristic order varying from N ϭ 4 at early times to N ϭ 9 at propagation speed is infinite. In the context of operator splitting later times.
formulations, it is the pressure solve which is the most computation-At elevated resolutions, the linear system which imposes ally challenging, despite its elliptic origins. We examine several preconditioners for the consistent L 2 Poisson operator arising in the pressure/divergence-free constraint at each time step the ސ N Ϫ ސ NϪ2 spectral element formulation of the incompressible can become very ill conditioned and consequently tends Navier-Stokes equations. We develop a finite element-based addito be the computational bottleneck when iterative solvers tive Schwarz preconditioner using overlapping subdomains plus are employed. This problem can be exacerbated by the a coarse grid projection operator which is applied directly to the presence of high-aspect-ratio elements and/or widely varypressure on the interior Gauss points. For large two-dimensional problems this approach can yield as much as a fivefold reduction ing scales of resolution which are frequently encountered in simulation time over previously employed methods based upon in practice, but often not present in model problems. Condeflation. ᮊ 1997 Academic Press sequently, all of our recent iterative development work has focused upon a suite of cylinder problems of the type shown in Fig. 1.