Analysis and implementation of a parallelization strategy on a Navier-Stokes solver for shear flow simulations

A parallel computational solver for the unsteady incompressible three-dimensional Navier± Stokes equations implemented for the numerical simulation of shear ¯ow cases is presented. The computational algorithms include Fourier expansions in the streamwise and spanwise directions, second-order centered ®nite di€erences in the direction orthogonal to the solid walls, third-order Runge±Kutta procedure in time in which both convective and di€usive terms are treated explicitly; the fractional step method is used for time marching. Based on the numerical algorithms implemented within the computational solver, three di€erent (MPI based) parallelization strategies are devised. The three schemes are evaluated with particular attention to the impact of the communications onto the whole computational procedure, and one of them is implemented. Computations are executed on two di€erent parallel machines and results are shown in terms of parallel performance. Processes using di€erent number of processors combined with di€erent number of computational grid points are tested.