A fully implicit parallel solver for viscous flows; numerical tests on high performance machines

Publisher Summary This chapter presents a parallel fully implicit flow solver for incompressible Navier-Stokes (INS) equations, written in terms of vorticity and velocity, and tests it on different distributed memory multiple instruction multiple data (MIMD) architectures. Governing equations are discretized by using a finite difference approach. Linear systems arising from discretization are solved by a parallel implementation of biconjugate gradient stabilized (Bi-CGSTAB) algorithm used in conjunction with a block incomplete LU factorization (BILU) as pre-conditioner. The chapter investigates a tough problem—the transition to unsteady regime in a reasonable computational time. It is shown that the code can be ported to a range of parallel hardware, being a good parallel efficiency and scalability on all tile machines considered. Worse performances in terms of elapsed time have been obtained on Cray, torus three-dimensional (T3D). Results are given for the simulation of a three-dimensional flow in a rectangular box heated from below. The chapter emphasizes the analysis of transition from steady to non periodic regime.