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

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• 作者：Marc Medale ; Bruno Cochelin
• 关键词：Path-following or continuation methods ; Direct solver for large scale algebraic systems ; Parallel computer implementation ; Rayleigh– ; Bé ; nard– ; Marangoni instability
• 刊名：Journal of Computational Physics
• 出版年：2009
• 出版时间：1 December 2009
• 年：2009
• 卷：228
• 期：22
• 页码：8249-8262
• 全文大小：2712 K

文摘

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.