# Control volume unstructured mesh procedure for convection-diffusion solidification processes

Chow, Peter M-Y
(1993)
*Control volume unstructured mesh procedure for convection-diffusion solidification processes.*
PhD thesis, University of Greenwich.

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## Abstract

The research work presented herein addresses the unstructured mesh problem in finite volume (FV) or control volume (CV) method used in numerical simulations. The modelling work conducted is in context of solidification for casting processes.

The control volume-unstructured mesh (CV-UM) method can be categorised into two approaches, a vertex-centred and a cell-centred approach. The classification of the approach is based on the relationship between the control volume and the unstructured mesh. The vertex-centred is naturally unstructured and has been used successfully in fluid flow and heat transfer calculations. The cell-centred on the other hand has always been associated with structured (quadrilateral) meshes, this has been extended to handle

unstructured mesh in the current work and is called the irregular control volume (ICV) method. Both approaches have been studied for solidification by conduction only, using

several standard phase change test cases and one with experimental data from the casting industry. The result of this work is reported and their suitability for solidification addressed.

For the ICV method, the extension to solve the full convective-diffusive solidification was undertaken, these are primarily the fluid flow and energy equations solved using the well known SIMPLE algorithm. One spin-off from the ICV is the appearance of "highorder cell" control volumes, control volumes with more than the standard four cell faces in two-dimensions. The high-order cell technique is exhibiting the same characteristics as high-order schemes used in standard CV method, when applied to standard CFD test cases. The one current drawback for the technique is the generation of these high-ordercells, currently no fully- or semi-automatic mesh generation is available. This prevented further study of the technique and used in the solidification test cases, where in one, experimental data is available for the phase change fronts. This was carried Out using quadrilateral meshes, but solved using the unstructured approach of the ICV. The predicted solution is in qualitative agreement with experiment.

The second convective-diffusive solidification problem is the first to demonstrate the CV-UM integrated framework by solving two major casting components simultaneously,

the solidification (the work undertaken in this research) and the residual stress for deformation. This is still an on going research work, where refinement and validation

are required and further integration of casting processes, such as mould filling, are necessary to complete the various stages of the shape casting process.

This kind of integrated simulation requires huge amount of computations, it will take days for traditional scalar computers to do one prediction. Vector and parallel machines

offer ways in which to bring down the computing times to a level that is in hours instead of days. To utilise machines with vector and parallel capability efficiently, the

algorithm of the model process need to be mapped onto such architectures for it to take full advantage of the computing powers. The solidification algorithm in threedimensions has been vectorised and a speed-up of five is possible.

This was part of a collective study into mapping algorithms Onto vector and parallel computers, where it emerged that the ideal computing architecture is a network of processors each with its own vector capabilities.

Item Type: | Thesis (PhD) |
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Additional Information: | uk.bl.ethos.334384 |

Uncontrolled Keywords: | applied mathematics,vectors, solidification, pure mathematics, applied mathematics, fluid mechanics |

Subjects: | Q Science > QA Mathematics T Technology > TJ Mechanical engineering and machinery |

School / Department / Research Groups: | School of Computing & Mathematical Sciences Faculty of Architecture, Computing & Humanities > School of Computing & Mathematical Sciences School of Computing & Mathematical Sciences > Centre for Numerical Modelling & Process Analysis Faculty of Architecture, Computing & Humanities > School of Computing & Mathematical Sciences > Centre for Numerical Modelling & Process Analysis |

Last Modified: | 16 Mar 2016 15:21 |

URI: | http://gala.gre.ac.uk/id/eprint/6133 |

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