Aston, John Geoffrey Liam; (1990) A direct approach to computer modelling of fluids. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

Conventional approaches to Computational Fluid Dynamics (CFD) are highly mathematical in content and presentation, and physical interpretation of the algorithms can often be obscure. This is believed to inhibit advances in the CFD field and the importance of such advances for Naval Architecture, as a particular application, is discussed. As a possible alternative to conventional methods, a "direct" approach to computer modelling of fluids is proposed where all the algorithms involved are "physically transparent" in that they avoid intermediate mathematical interpretations. Rules for the development of such a model are formulated, and a programming strategy, which advocates modularising the algorithms to reflect the cause and effect mechanisms in real fluids, is outlined. The principles of the direct modelling approach are demonstrated in the development of a computer program for 2-dimensional, incompressible, inviscid flows. The technique requires that the total pressure in a flow is decomposed into two principal components, the temporal pressure and the convective pressure, associated respectively with the temporal and convective accelerations of the fluid. The model incorporates a numerically "explicit" pressure spreading algorithm for determining the temporal pressure and acceleration responses to external disturbances. The actual compressibility of the "incompressible" fluid is modelled via the bulk modulus. Convective pressure is synthesised as flow develops by accounting for the small spatial variations in the fluid's density associated with the temporal pressure field. Simple internal flows, and the acceleration of bodies at or near a free-surface, have been modelled successfully. Flows with a finite free-surface distortion or system geometry change will require the incorporation of grid re-generation algorithms for the spatial discretisation. Routes for future developments, including viscous modelling, are discussed. Apart from potential advantages for CFD, the direct approach should benefit general fluid dynamics education since the concepts involved promote a better understanding of fluid behaviour.

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