This work is concerned with the development of reliable and versatile computational tools for the numerical simulation of two-dimensional heat conduction and incompressible and compressible laminar fluid flow problems. Issues related to adaptive techniques, discretisation methodologies (upwind or centred type) and the design of high-resolution shock-capturing schemes are investigated in this thesis. Three distinct research works have been pursued here. In the first work, attention is focused on the construction of an adaptive finite element procedure with mesh refinement, by mesh enrichment, in time and space, and with automatic time stepping for the heat conduction problem in a stationary medium. The Galerkin finite element method and the Euler-backward time marching scheme are used as the basis to obtain the steady-state and transient approximate solutions. Particular emphasis concentrates on the design of the adaptive strategy and the combined influence of time and spatial adaptation. The second task is concerned with the derivation of adaptive remeshing strategies for both steady and unsteady solution of the incompressible Navier-Stokes equations in primitive variables. A Petrov-Galerkin formulation, which automatically introduces streamline upwinding and allows equal order interpolation for all variables, combined with either an explicit or implicit time integration represents the general discretisation methodologies adopted. The adaptive redefinition of the mesh, the error estimate and specific features, such as the presence of singularities on the solution and accumulation of interpolation errors inherent to a transient remeshing, are carefully analysed with some remedies proposed to deal with such difficulties. In the final part of the thesis, the most relevant mathematical-physical properties of the first order hyperbolic model equations are discussed. The utilisation of upstream or centred discretisation and several ways to produce high-resolution schemes to deal with this class of problems are described and compared for one-dimensional test cases. With regard to upwind discretisation techniques, the most popular flux difference splitting, flux vector splitting and some recently proposed hybrid splitting methodologies are considered.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:637967 |
| Date | January 1995 |
| Creators | Lyra, P. R. M. |
| Publisher | Swansea University |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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