A parallel computer implementation of the Asymptotic Numerical Method to study thermal convection instabilities

Authors:
Marc Medale;Bruno Cochelin
Affiliations:
IUSTI, UMR 6595 CNRS-Université Aix-Marseille, 5 rue Enrico Fermi, Technopole de Chíteau-Gombert, 13453 Marseille Cedex 13, France;LMA, UPR 7051 CNRS, 38 rue Frédéric Joliot Curie, Technopole de Chíteau-Gombert, 13451 Marseille Cedex 20, France
Venue:
Journal of Computational Physics
Year:
2009

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Abstract

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-Benard-Marangoni convection and its related cellular pattern.