Efficient Vectorized Finite-Difference Method to Solve the Incompressible Navier–Stokes Equations for 3-D Mixed-Convection Flows in High-Aspect-Ratio Channels

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-Bénard flows with steady longitudinal, unsteady transverse, and convectively unstable wavy rolls.

Acknowledgments

Dr. E. Chénier and Dr. H. Pabiou are greatly acknowledged for numerous helpful discussions. All the computations were carried out on the NEC-SX5 supercomputer at IDRIS (Orsay, France) under Research Project 41474. The present work is supported by the French government through a Pluri-Formation Plan (PPF) on “Instabilities and transitions in thermoconvective flows in complex situations.”