Three-dimensional Computations of Time-dependent Incompressible Flows with an Implicit Multigrid-driven Algorithm on Parallel Computers

The present work is aimed at the development of a robust, computationally efficient algorithm for the simulation of unsteady incompressible flows of interest in engineering. In particular, we focus on the extension of a fully-implicit multigr~d driven algorithm, orig/nally proposed and vaJhdated for both the two-dimensional Euler and Navier-Stokes equations in references [1,2], to three dimensions. The vortex shedding from a circular cyhnder has been recently investigated by a number of authors with the focus on the mechanism of momentum and vorticity transport [4, 5] and on the active control of the wake structure [6]. The transition of the flow to a threedimensional mode (180 < Re < 260) attracts particular interest. In this regime the slow asymptotics of the wake provides a challenging test for numerical methods since long integration times are necessary to resolve the flow evolution toward a limiting cycle. In the present work, time-resolved computations of vortex shedding from a circular cylinder for Reynolds numbers between 45 and 250 are performed to assess both accuracy and parallel efficiency of the present algorithm. The vortex wake structure as well as the averaged flow quantities for this flow regime are found to be in a good agreement with the experimental and computational data, obtained by other authors.