Analysis and implementation of 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 flow cases is presented. The computational algorithms include Fourier expansions in the streamwise and spanwise directions, second-order centered finite differences in the direction orthogonal to the solid walls, third-order Runge–Kutta procedure in time in which both convective and diffusive terms are treated explicitly; the fractional step method is used for time marching. Based on the numerical algorithms implemented within the computational solver, three different (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 different parallel machines and results are shown in terms of parallel performance. Processes using different number of processors combined with different number of computational grid points are tested.