Passmore, Tim and Roberts, A. J. (2003) Low Prandtl number fluid convection modelled using symbolic algebra (REDUCE) and Matlab. In: ANZIAM 2003: Computational Techniques and Applications, 16-18 Jul 2003, Toowoomba, Australia.
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Official URL: http://anziamj.austms.org.au/V44/CTAC2001/Pass
Using the Boussinesq approximation for a fluid of low Prandtl number, a low dimensional model of the onset of Rayleigh-Benard convection is developed. The initial roll mode instability is considered for a fluid, heated from below, between parallel, horizontal, non-slip, constant-temperature boundaries. Centre manifold theory provides a way of constructing a low dimensional model of the resulting two dimensional flow. Computer algebra implemented in reduce is used to symbolically expand the centre manifold as an asymptotic series in the convective amplitude. The spatial structure functions in this expansion are then found numerically in Matlab. A feature of this approach is that code output from reduce is used, with only minor syntactic editing, as the Matlab code to perform the numerical iteration. Thus a coding task which would have been difficult by hand is easily automated. The technique is generally applicable to perturbation expansions and its computational advantages over more formal Galerkin type expansions are discussed.
|Item Type:||Conference or Workshop Item (Commonwealth Reporting Category E) (Paper)|
|Additional Information:||Electronic Supplement 2002-3. Author's version unavailable.|
|Uncontrolled Keywords:||low Prandtl number; Matlab; equations; motion; manifold theory; fluid dynamics; linear analysis|
|Fields of Research (FOR2008):||01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations|
01 Mathematical Sciences > 0101 Pure Mathematics > 010108 Operator Algebras and Functional Analysis
01 Mathematical Sciences > 0102 Applied Mathematics > 010204 Dynamical Systems in Applications
|Subjects:||230000 Mathematical Sciences > 230100 Mathematics|
|Socio-Economic Objective (SEO2008):||E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences|
|Deposited On:||11 Dec 2009 14:24|
|Last Modified:||03 Oct 2011 17:01|
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