Efficient vectorized finite-difference method to solve the incompressible navier-stokes equations for 3-D mixed-convection flows in high-aspect-ratio channels

TL;DR: In this article, a very efficient vectorized code is tailored to solve 3D incompressible Navier-Stokes equations for mixed-convection flows in high streamwise aspect ratio channels.

Abstract: A very efficient vectorized code is tailored to solve 3-D incompressible Navier-Stokes equations for mixed-convection flows in high streamwise aspect ratio channels. It is based on Goda's algorithm, second-order finite differences, an incremental factorization method of alternating direction implicit (ADI) type, spectral decomposition of the 1-D Laplace operators, and the tridiagonal matrix algorithm (TDMA). It is shown to be of second order in both space and time by a general method of determining code convergence orders and to have good performance on a NEC-SX5 supercomputer. It is validated through experiments of various Poiseuille-Rayleigh-Benard flows with steady longitudinal, unsteady transverse, and convectively unstable wavy rolls.