| Summary: | This thesis is an investigation into the modelling of compressible viscoelastic fluids. It can be divided into two parts: (i) the development of continuum models for compressible and nonisothermal viscoelastic fluids using the generalised bracket method and (ii) the numerical modelling of compressible viscoelastic flows using a stabilised finite element method. We introduce the generalised bracket method, a mathematical framework for deriving systems of transport equations for viscoelastic fluids based on an energy/entropy formulation. We then derive nonisothermal and compressible generalisations of the Oldroyd-B, Giesekus and FENE-P constitutive equations. The Mackay-Phillips (MP) class of dissipative models for Boger fluids is developed within the bracket framework, complimenting the class of phenomenological models that already exist in the literature. Advantages of the MP models are their generality and consistency with the laws of thermodynamics. A Taylor-Galerkin finite element scheme is used as a basis for numerical simulations of compressible and nonisothermal viscoelastic flow. Numerical predictions for four 2D benchmark problems: lid-driven cavity flow, natural convection, eccentric Taylor-Couette flow and axisymmetric flow past a sphere are presented. In each case numerical comparisons with both empirical and numerical data from the literature are presented and discussed. Numerical drag predictions for the FENE-P-MP model are presented, displaying good agreement with both numerical and experimental data for the drag behaviour of Boger fluids.
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