A parallel computer implementation of the asymptotic numerical method to study thermal convection instabilities

Marc Medale (1) , Bruno Cochelin (2)

1 IUSTI - Institut universitaire des systèmes thermiques industriels
2 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]

We have developed a numerical model to efficiently compute steady-state combined buoyancy and thermocapillary convection solutions. It features a parallel computer implementation of an Asymptotic Numerical Method to perform steady-state path-following and locate bifurcation points in problems involving large size algebraic systems, up to few million degrees of freedom. The model has been first validated on a problem for which a reference solution exists and then is used to analyse the influence of the container size and shape on Rayleigh–Bénard–Marangoni convection and its related cellular pattern.

Mots clés: Path-following or continuation methods Direct solver for large scale algebraic systems Parallel computer implementation Rayleigh–Bénard–Marangoni instability

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Mécanique [physics.med-ph]; Mécanique des structures [physics.class-ph]; Mécanique des structures [physics.class-ph]

Marc Medale, Bruno Cochelin. A parallel computer implementation of the asymptotic numerical method to study thermal convection instabilities. Journal of Computational Physics, 2009, 228 (22), pp.8249-8262. ⟨10.1016/j.jcp.2009.07.032⟩. ⟨hal-00487339⟩