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

Abderrahmane Benzaoui (1) , Xavier Nicolas (1, 2) , Shihe Xin (3)

1 LETEM - Laboratoire d'Etudes des Transferts d'Energie et de Matière
2 MSME - Laboratoire de Modélisation et Simulation Multi Echelle
3 LIMSI - Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur

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.

Mots clés: vectorial computation; high aspect ratio : channel flow; mixed convection; vectorized algorithm; Poiseuille flow; Rayleigh-Bénard; rectangular channel

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Modélisation et simulation

Abderrahmane Benzaoui, Xavier Nicolas, Shihe Xin. Efficient vectorized finite-difference method to solve the incompressible navier-stokes equations for 3-D mixed-convection flows in high-aspect-ratio channels. Numerical Heat Transfer, Part B Fundamentals, 2005, 48 (3), pp.277-302. ⟨10.1080/10407790590959825⟩. ⟨hal-00694583⟩