CSR 1-2004 Computation of Incompressible and Weakly-Compressible Viscoelastic Liquids Flow: finite element/volume schemes
M. F. Webster, I. J. Keshtiban, and F. Belblidia
In this study, we analyse viscoelastic numerical solution for an Oldroyd-B model under incompressible and weakly-compressible liquid flow conditions. We consider flow through a planar four-to-one contraction, as a standard benchmark, throughout a range of Weissenberg numbers up to critical levels. At the same time, inertial and creeping flow settings are also addressed.
Within our scheme, we compare and contrast, two forms of stress discretisation, both
embedded within a high-order pressure-correction time-marching formulation based on
triangles. This encompasses a parent-cell finite element/SUPG scheme, with quadratic stress
interpolation and recovery of velocity gradients. The second scheme involves a sub-cell finite
volume implementation, a hybrid fe/fv scheme for the full system.
A new feature of this study is that both numerical configurations are able to accommodate
incompressible, and low to vanishing Mach number compressible liquid flows. This is of
some interest within industrial application areas. We are able to provide parity between the
numerical solutions across schemes for any given flow setting. Close examination of flow
patterns and vortex trends indicates the broad differences anticipated between incompressible
and weakly-compressible solutions. Vortex reduction with increasing Weissenberg number is
a common feature throughout. Compressible solutions provide larger vortices (salient and lip)
than their incompressible counterparts, and larger stress patterns in the re-entrant corner
neighbourhood. Inertia tends to reduce such phenomena in all instances. The hybrid fe/fvscheme
proves more robust, in that it captures the stress singularity more tightly than the feform
at comparable Weissenberg numbers, reaching higher critical levels. The sub-cell
structure, the handling of cross-stream numerical diffusion, and corner discontinuity capturing
features of the hybrid fe/fv-scheme, are all perceived as attractive additional benefits that give
preference to this choice of scheme.
Report Titles
CSR 2-2004 Compressible Flow Solvers for Low Mach Number Flows Ð a review
I.J. Keshtiban, F. Belblidia and M.F. Webster
The low Mach number setting is a singular limiting situation in compressible flows.
As Mach number approaches zero, compressible (density-based) flow solvers suffer
severe deficiencies, both in efficiency and accuracy. There are two main approaches
advocated in the development of algorithms for the computation of low Mach number
flows; first, There is the modification of compressible solvers (density-based)
downward to low Mach numbers; second, extending incompressible solvers (pressurebased)
towards this regime. Here, we present a brief review of the literature in this
area. This addresses the modifications necessary to effectively apply density-based
schemes and develop compressible pressure-based schemes to such low Mach number
configurations.
Report Titles
CSR 3-2004 Modelling Pom-Pom Type Models with High-Order Finite Volume Schemes
M. Aboubacar, J. P. Aguayo, P.M. Phillips, T.N.Phillips, H. R. Tamaddon-Jahromi B.A. Snigerev and M.F. Webster
We are concerned with the numerical solution of viscoelastic flows using
two contrasting high-order finite volume schemes. We take our earlier work
for transient start-up flow in a channel and extend this beyond Oldroyd-B
modelling to consider a different fluid model of the pom-pom class.
This includes Single Extended form of the Pom-Pom model (SXPP),
comparing the results of two different finite volume schemes.
The numerical techniques employed are time-stepping algorithms, one
of hybrid finite element/volume type, the other of pure finite volume form.
The pure finite volume scheme is a staggered-grid cell-centred scheme based
on area-weighting and a semi-Lagrangian formulation. This may be implemented
on structured or unstructured rectangular grids, utilising backtracking along
the solution characteristics in time. For the hybrid scheme, we solve the
momentum/continuity equations by a fractional-staged
Taylor-Galerkin/pressure-correction procedure and invoke a cell-vertex finite
volume scheme for the constitutive law. This draws upon fluctuation distribution
schemes (upwinding), different combinations of 'flux' and 'median-dual-cell'
spatial discretisations and time-term treatments. Here, unstructured and
structured meshes may be used, based largely on triangular grids. A
comparison of the two finite volume approaches will be presented,
concentrating upon the new features posed by the pom-pom class of models.
Report Titles
CSR 4-2004 Sub-cell approximations for viscoelastic flows-filament stretching
M.F. Webster, H. Matallah and K.S. Sujatha
The accuracy, stability and consistency of new stress interpolation schemes is
investigated, based upon sub-cell approximations. This includes the contrast of two
alternative hybrid spatial discretisations: a cell-vertex finite element/volume (fe/fv)
scheme and a finite element equivalent (fe). Here, the interest is to explore the
consequences of utilizing conventional methodology and to demonstrate resulting
drawbacks in the presence of complex stress equation source terms. Alternative strategies
worthy of consideration are presented for a constant shear viscosity model, that of
Oldroyd-B, with strain-hardening and unbounded extensional properties. We demonstrate
how high-order accuracy may be achieved by respecting consistency in our algorithmic
constructions.
Both fe- and fv-spatial discretisations are embedded within this methodology. Linear
interpolation for stress, of either fe- or fv-form on triangular sub-cells, is referenced
within parent triangular finite elements in two dimensions. Finite element discretization is
employed for the momentum and continuity system, via a second-order pressurecorrection
scheme. In this regard, a complex filament-stretching flow with a free-surface
is selected to compute the transient evolution of kinematic and stress fields.
Shortcomings of various up-winding schemes are discussed, whilst dealing with such
free-surface type problems and appropriate strategies for dealing with these types of
problems are outlined.
Report Titles
CSR 5-2004 Computations via experiments with kinematic systems
E.J. Beggs and J.V. Tucker
Consider the idea of computing functions using experiments with kinematic systems.
We prove that for any set A of natural numbers there exists a 2-dimensional
kinematic system B_A with a single particle P whose observable behaviour
decides if
n is in A for all n in N. The system is a bagatelle and can be designed to operate under
(a) Newtonian mechanics or (b) Relativistic mechanics. The theorem proves that
valid models of mechanical systems can compute all possible functions on discrete
data. The proofs show how any information (coded by some A) can be embedded in
the structure of a simple kinematic system and retrieved by simple observations of its
behaviour. We reflect on this undesirable situation and argue that mechanics must
be extended to include a formal theory for performing experiments, which includes
the construction of systems. We conjecture that in such an extended mechanics the
functions computed by experiments are precisely those computed by algorithms. We
set these theorems and ideas in the context of the literature on the general problem
ÒIs physical behaviour computable?Ó and state some open problems.
Report Titles
CSR 6-2004 Automated office-management and interactive database Systems for the WWW
J. Harvey and M.F. Webster
This paper outlines the provision and development of interactive database systems through the context of the www,
providing a tiered-system of permissions, interaction and automation, and illustrated through a particular case-study.
Novel developments such as the multiple-view and multiple-edit facilities, coupled with system intelligence and data
integrity protocols, ensure the delivery of an efficient automated environment. This provides a solution with the power to
cater for the transparent delivery of document and multimedia services to a hierarchy of system users.
Report Titles
CSR 7-2004 Transient viscoelastic flows in planar contractions
M.F. Webster, H.R.Tamaddon-Jahromi and M. Aboubacar
This article considers transient flows for planar contractions and
Oldroyd-B fluids, with increasing flow-rate boundary conditions. We employ
a novel hybrid finite volume/element time-dependent algorithm. This scheme is
shown to be second-order accurate in space and time.
The hybrid scheme consists
of a Taylor-Galerkin finite element discretisation, and a cell-vertex
fluctuation-distribution finite volume approach. These two approaches
are coupled at each time-step to solve the parabolic/hyperbolic
system of partial differential equations. The finite element section
is applied to the mass and momentum conservation equations, whilst
the hyperbolic constitutive equation is treated via finite volume
discretisation. The application of this time-accurate scheme to complex
flows reveals some novel features, in contrast to
time-independent (constant flow-rate) driving boundary conditions.
In particular, we highlight dynamic flow structure evolution on the
field and in stress.
Report Titles
CSR 8-2004 Stabilisation of computations for incompressible and compressible liquid flows
F. Belblidia, I.J. Keshtiban and M.F. Webster
We analyse the effect of strain-rate stabilisation embedded within a
high-order pressure-correction time-marching formulation. This is applied
to a planar 4:1 abrupt contraction problem for an Oldroyd-B model under
incompressible and compressible flow conditions. We emphasize the
differences between non-stabilised and stabilised solutions through stress
profiles and limiting levels of critical We. It is observed that SRS
promotes the critical We-level by reducing stress oscillations and peak
stress-level around the re-entrant corner. Examination of flow patterns,
stress profiles and vortex characteristics highlight the key differences
between comparable incompressible and compressible solutions. In this
regard, compressible solutions tend to suppress stress oscillations, though
with attendant increase in peak stress-levels.
Report Titles
CSR 9-2004 The Numerical Prediction of Viscoelastic Flows using the Pom-Pom Model and High-Order Finite Volume Schemes
J.P. Aguayo, P.M. Phillips, T.N. Phillips, B.A. Snigerev, H.R. Tamaddon-Jahromi, and M.F. Webster
This study investigates the numerical solution of viscoelastic flows using two contrasting high-order
finite volume schemes. We extend our earlier work for Poiseuille flow in a planar channel and a Single
Extended Pom-Pom (SXPP) model [1], to determine steady-state solutions for planar 4:1 sharp
contraction flows. The numerical techniques employed are time-stepping algorithms: one of hybrid finite
element/volume type, the other of pure finite volume form. The pure finite volume scheme is a staggeredgrid
cell-centred scheme based on area-weighting and a semi-Lagrangian formulation. This may be
implemented on structured or unstructured rectangular grids, utilising backtracking along the solution
characteristics in time. For the hybrid scheme, we solve the momentum-continuity equations by a
fractional-staged Taylor-Galerkin pressure-correction procedure and invoke a cell-vertex finite volume
scheme for the constitutive law. A comparison of the two finite volume approaches will be presented,
concentrating upon the new features posed by the Pom-Pom class of models in this complex flow.
Report Titles
CSR 10-2004 Time-Dependent Algorithms for Viscoelastic Flow - finite element/volume schemes
M.F. Webster, H.R. Tamaddon-Jahromi and M. Aboubacar
Hybrid finite volume/element methods are investigated within the context of transient vis-
coelastic flows. A finite volume algorithm is proposed for the hyperbolic constitutive equation,
of Oldroyd-form, whilst the continuity/momentum balance is accommodated through a Taylor-
Galerkin finite element method. Various finite volume combinations are considered to derive
accurate and stable implementations. Consistency of formulation is key, embracing fluctuation
distribution and median-dual-cell constructs, within a cell-vertex discretisation on triangles. In
addition, we investigate the effect of treating the time-term in a finite element fashion, using
mass-matrix iteration instead of the standard finite volume mass-lumping approach. We devise an accurate
transient scheme that captures the analytical solution at short and long time,
both in core flow and near shear boundaries. In this respect, some difficulties are highlighted.
A new method emerges, with the Low Diffusion B (LDB, with or without mass-matrix iteration) as the optimal choice.
We progress to a complex flow application and demonstrate some
provocative features due to the in¡uence of true transient boundary conditions on evolutionary
flow-structure in a 4:1 start-up rounded-corner contraction problem.
Report Titles
CSR 11-2004 Managing Interaction for Multimedia Collaboration: Through the Keyhole of Noughts and Crosses Games
Siti Z. Z. Abidin, Min Chen and Phil W. Grant
Interaction management is concerned with the protocols
that govern structured interactive activities among multiple
users or agents in distributed and collaborative environments.
Research in this area has largely been carried
out in specific application domains, such as 3D virtual environments.
We present an abstraction of various collaborative
applications in the form of variations of noughts and
crosses. We examine the needs in these games for programming
interaction protocols, and propose a comprehensive
collection of program constructs for supporting interaction
management. We demonstrate, through these variations of
the game, the usefulness of these language constructs.
Report Titles