Effects of parallel strategies in the transitional flow investigation

Abstract

The direct numerical simulation of transitional and turbulent incompressible flows is an area that is increasing with the advance in computational resources. Code parallelization has became a useful tool in these simulations. In the present paper the unsteady two dimensional Navier–Stokes equations are used as physical model. Tollmien–Schlichting waves propagating in a Poiseuille flow is adopted as test case. Three frequencies showing different behavior according to the linear stability theory (LST) are used: unstable, nearly neutral and stable waves. The parallelization is done via domain decomposition in the streamwise direction. The time derivative is integrated by a classical fourth-order Runge–Kutta method. High-order compact finite difference schemes are used for the spatial derivatives discretization. The Poisson equation is solved by multigrid methods. The present paper explores different parallelization techniques for solving the tridiagonal system, and the multigrid method. The results are compared with LST, and also between the different parallel strategies to show the advantages and disadvantages of each one.