# Low Prandtl number fluid convection modelled using symbolic algebra (REDUCE) and Matlab

Paper

*ANZIAM 2003: Computational Techniques and Applications.*Toowoomba, Australia 16 - 18 Jul 2003 Cambridge, United Kingdom .

Paper/Presentation Title | Low Prandtl number fluid convection modelled using symbolic algebra (REDUCE) and Matlab |
---|---|

Presentation Type | Paper |

Authors | Passmore, Tim (Author) and Roberts, A. J. (Author) |

Journal or Proceedings Title | ANZIAM Journal |

Australia and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal | |

Journal Citation | 44, pp. C590-C626 |

Number of Pages | 36 |

Year | 2003 |

Place of Publication | Cambridge, United Kingdom |

ISSN | 1446-1811 |

1446-8735 | |

Web Address (URL) of Paper | http://anziamj.austms.org.au/V44/CTAC2001/Pass |

Conference/Event | ANZIAM 2003: Computational Techniques and Applications |

Event Details | ANZIAM 2003: Computational Techniques and Applications Event Date 16 to end of 18 Jul 2003Event Location Toowoomba, Australia |

Abstract | 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. |

Keywords | low Prandtl number; Matlab; equations; motion; manifold theory; fluid dynamics; linear analysis |

ANZSRC Field of Research 2020 | 490303. Numerical solution of differential and integral equations |

490408. Operator algebras and functional analysis | |

490105. Dynamical systems in applications | |

Public Notes | Electronic Supplement 2002-3. Author's version unavailable. |

Byline Affiliations | Department of Mathematics and Computing |

https://research.usq.edu.au/item/9yzqx/low-prandtl-number-fluid-convection-modelled-using-symbolic-algebra-reduce-and-matlab

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