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Title: Numerical simulation of compressible viscoelastic flows
Author: Jalili Keshtiban, E.
Awarding Body: University of Wales Swansea
Current Institution: Swansea University
Date of Award: 2005
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In this work, we first present a brief introduction to flow at low Mach numbers, followed by rheological and equations of states for dense materials. Subsequently, we provide the background theory over several difficult issues encounter by compressible schemes, at low Mach numbers (singular limit of compressible flows). This would include key modifications employed to rectify density-based schemes and extending pressure-based incompressible algorithms for dealing with compressible flows. To accommodate weakly-compressible viscoelastic/viscous flows at low Mach numbers, a high-order time-marching pressure-correction algorithm has been adopted, in semi-implicit form. For discretisation of velocity and pressure equations, over the fractional stages of this pressure correction scheme, a Galerkin finite element was employed. To accommodate stress equations (considered here in Oldroyd-B form) two spatial discretisation alternatives are adopted. This encompasses a mixed finite element formulation in SUPG form, with a quadratic stress and velocity interpolations. The second scheme involves a sub-cell finite volume implementation, a hybrid fe/fv scheme for the full system. For both scheme variants, enhanced velocity gradients are acquired, via a recovery technique. Two discrete representations are proposed to interpolate density: a piecewise-constant form with gradient recovery and a linear interpolation form, akin to that on pressure. Validation on a numbers of classical benchmark problems bear out the high quality of performance of both compressible flow implementations, at low to vanishing Mach number. Neither linear, nor constant density interpolation schemes degrade the second-order accuracy of the original incompressible fractional-staged pressure-correction scheme. In viscous context, we conduct several tests on cavity and contraction flows (both Cartesian and cylindrical coordinates) for both compressible and incompressible flow settings. To validate results of our original incompressible scheme, for the cavity test problem, we compare and contrast predicted velocity fields with those in the literature. For this test problem, the effect of singularity in boundary conditions is investigated on spatial accuracy for both incompressible and compressible flows with the two density interpolations. On contraction flows, consistency is confirmed according to the two different forms of density interpolation. Capability of the scheme in dealing with very low Mach number flows is demonstrated, via adjusting Tait parameters. The scheme responses well as Mach number approaches zero (incompressible limit), and there is no obvious minimum threshold on Mach number for this scheme. We have conducted several tests, under the compressible settings on the effect of system eigenvalues on convergence patterns.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available