CSR 1-2005 Stabilised Computations for Incompressible and Mildly Compressible Viscoelastic Flows
F. Belblidia, I.J. Keshtiban and M.F. Webster
We analyse and contrast different stabilisation methodologies embedded within a time-marching incremental pressure-correction
formulation. Numerical solutions are presented for an Oldroyd-B model under incompressible and mildly compressible settings,
considering flow through a planar four-to-one abrupt-contraction. Three alternative stabilisation strategies are analysed to
hone the response of the base hybrid finite element/volume (fe/fv)-implementation: a temporal stabilisation procedure
(TSS, a theoretical counterpart to Galerkin Least-Squares, GLS); a discontinuity capturing procedure (RCI,
reduced corner integration); and a strain-rate stabilisation procedure (SRS, to satisfy LBB-conditions).
To reflect the stabilised properties of each scheme, the study interrogates levels of stable Weissenberg number
(We) solution, vortex activity, stress field structure about abrupt corners and in boundary layers, and cross-stream
solution representation. Combinations of these stabilisation variants are proposed to seek optimal stability properties.
We consider the specific effect that inclusion of compressibility has, contrasting this against its incompressible counterpart.
Results indicate that most improvement has been encountered with the SRS-scheme, where Wecrit-levels have more than doubled above
neutral variants, while stress peaks levels have been constrained. At a selected We-level and under a specific flow setting,
all scheme variants have produced similar salient-corner vortex behaviour, predicting vortex reduction under increasing We.
In contrast, lip-vortex features are found to be significantly affected by the particular re-entrant corner treatment applied. When
present, lip vortices grow with increasing We.
Report Titles
CSR 2-2005 A short note on pressure-correction schemes: TGPC and CBS
F. Belblidia, I.J. Keshtiban and M.F. Webster
In the computation of viscoelastic flows, satisfaction of inf-sup conditions plays a crucial role. Introducing stress into the Stokes system imposes additional compatibility conditions between the various trial-function spaces, to be employed for spatial approximation. This is particularly so between stress and velocity gradients. At first glance, it would appear attractive to inherit a basis devoid of inf-sup velocity-pressure conditions and extend this with appropriate side-conditions to the viscoelastic context. This is the fulcrum of the present article, remaining within the viscous setting for investigation.
In recent years, claims have emerged for pressure-correction based schemes, that one may circumvent the need for satisfaction of inf-sup conditions by removing pressure from the velocity-prediction stage, instead transforming dependency upon pressure-update and velocity-correction stages. The characteristic-based splitting scheme (CBS) has been established upon this premise and employed successfully with linear equal-order elements (P1P1).
Within the present study, CBS and TGPC-approaches have been compared and contrasted, the latter being a Taylor-Galerkin pressure-correction scheme. The TGPC scheme has been employed to solve various flow problems, particularly for highly-viscous, viscoelastic flows. Here, two viscous test problems have been considered. First, for a Couette flow, where the velocity assumes linear-shaped profiles with constant (vanishing) pressure. Second, for a Poiseuille flow, in which velocity and pressure profiles adopt quadratic and linear forms, respectively. Such solutions may be employed to distinguish between P1P1 and P2P1-representations, in a numerical quantitative sense.
It has been demonstrated that CBS-schemes, when based on P2P1 elements and applied to pressure-driven flows
(Poiseuille), encounter severe numerical discretisation error. This arises in the form of large spatial oscillations
across the field and through proper specification of auxiliary (velocity) variables. Alternatively, we have demonstrated
the superiority of the TGPC-scheme structure in dealing with such pressure-driven viscous flows. The differences are marked
and strongly advocate the TGPC choice, being suitable for extension into the viscoelastic regime.
Report Titles
CSR 3-2005 Newtonian systems, bounded in space, time, mass and energy can compute all functions
E.J. Beggs and J.V. Tucker
First, we prove that for any set A of natural numbers there exists a 3-dimensional Newtonian kinematic system M_A, with an infinite family of particles Pn whose total mass is bounded, and whose observable behaviour can decide whether or not n is in A for all n in N in constant time. In particular, the theorem implies that simple Newtonian mechanical systems that are bounded in space, time, mass and energy can compute all possible functions on discrete data.
Secondly, we reflect on the nature of experimental computation. The proof of
the theorem shows how any information (coded by some A) can be embedded in
the static structure of simple kinematic equipment and retrieved by a simple experimental
procedure. This suggests that the idea of equipment is problematic
when computing under Newtonian mechanics. We argue that a formal theory for
experimental computation needs restrictive conditions on the notion of experimental
procedure and the construction of equipment. We conjecture that using such
a restricted mechanics the functions computed by experimental computation are
equivalent to those computed by algorithms, i.e. the partial computable functions.
Report Titles
CSR 4-2005 Designing Interaction and Interest Management Protocols using 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 networked collaborative environments. Interest management is concerned with the relevance-based data ltering in networked collaborative environments. The main objective is to avoid broadcasting data unless it is to be shared by all the processes, and to provide secured data transmission of a subset of information relevant to each process. The research in these two important aspects of networked software has largely been carried out in speci c application domains, such as agent-based systems and 3D virtual environments.
In this paper, we present an abstraction of various collaborative applications in the form
of the noughts and crosses game and its variations. We examine the needs in these games
for programming interaction protocols and data ltering mechanisms, and propose a comprehensive
collection of program constructs for supporting interaction and interest management.
We report our efforts for incorporating these new constructs into JACIE (Java-based
Authoring language for Collaborative Interactive Environments), a scripting language designed
to support rapid prototyping and implementation of collaborative applications. We
demonstrate, through variations of the noughts and crosses game, the usefulness of these
language constructs.
Report Titles
CSR 5-2005 Conjunctive normal forms with non-boolean variables, autarkies and hypergraph colouring
Oliver Kullmann
We investigate in depth the properties of a natural generalisation, called
Òsets of no-goodsÓ in the AI literature, of boolean formulas in conjunctive
normal forms such that non-boolean variables can be used. After building
up a solid foundation, we generalise the notion of deficiency, and we obtain
polynomial time satisfiability decision for generalised clause-sets with fixed
maximal deficiency (generalising the boolean case, where the deficiency is the
difference between the number of clauses and the number of variables). The
main tool here is autarky theory (where autarkies are generalisations of satisfying
assignments), and we concentrate especially on matching autarkies (based
on matching theory) and special cases of linear autarkies (based on linear
programming and linear algebra). As an application we study the problem of
hypergraph colouring, considering early results of P.D. Seymour on the number
of edges in minimally non-2-colourable hypergraphs, which are reinterpreted
and generalised in the light of autarky theory.
Report Titles
CSR 6-2005 The Numerical Prediction of Planar Viscoelastic Contraction Flows using the Pom-Pom Model and Higher-Order Finite Volume Schemes
J. P. Aguayo, P. M. Phillips, T. N. Phillips, H.R. Tamaddon-Jahromi , B. A. Snigerev, 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 the single equation
form of the extended pom-pom (SXPP) model, 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 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. A comparison of the two finite volume approaches is presented,
concentrating upon the new features posed by the pom-pom class of models in this context of non-smooth flows.
Report Titles
CSR 7-2005 Computational Predictions for Viscoelastic Filament Stretching Flows: ALE methods and free-surface techniques (CM and VOF)
K.S.Sujatha, H.Matallah, J.Banaai and M.F.Webster
This article considers the dynamics of filament stretching for viscoelastic liquids.
We investigate the consequences of employing both fe and fv spatial discretisations
within an incremental pressure-correction scheme, considering various meshmovement
and free-surface tracking techniques. Finite element discretisation is
employed for the momentum and continuity equation, whilst a pure-upwinding cellvertex
finite volume representation is utilised for the hyperbolic stress equation.
Compressive mesh procedures outperform volume-of-fluid counterparts, and when
coupled to an ALE-formulation governing mesh movement, provide a powerful
technique to access impressively large Hencky-strains. If precision in determination
of free-surface curvature is demanded, a particle-tracking approach is shown to be
preferable to a kinematic condition for surface-level. Results of the study lie in close
agreement with the literature in trends and measures of Trouton ratio, minimum
radius and extensional viscosity predictions.
Report Titles
CSR 8-2005 Extensional response of the pom-pom model through planar contraction flows for branched polymer melts
J. P. Aguayo, H. R. Tamaddon-Jahromi, M. F. Webster
One objective of this study is to assess the in
uence of the number of dangling
arms at each end of the pom-pom molecule on
ow characteristics in a 4:1 planar
rounded-corner contraction, where varying the number of arms a ects the level of
entanglement in the system. For these complex
ows, we evaluate the major in
uence
of extensional viscosity and Trouton ratio when comparing kinematic-based as
opposed to phenomenological network-based models. The stability of the proposed
extended pom-pom model (XPP) is investigated for a range of Weissenberg numbers
utilising a Hybrid nite element/volume scheme. For this scheme, we solve the
momentum/continuity equations by a fractional-staged Taylor-Galerkin/pressurecorrection
procedure and invoke a cell-vertex
uctuation-distribution nite volume
scheme for the constitutive law. Distinction may be drawn between
uid response
in the extension-hardening regime and those displaying a degree of softening. In
particular, trends in salient-corner vortex-intensity response can be associated with
the extensional properties of the extended version of the pom-pom model. Critical
levels of solution elasticity attainable depend on precise extensional viscosity
characteristics. The in
uence of various model parameters upon eld response is
described through, rates of deformation, stress and stretch.
Report Titles
CSR 9-2005 Modelling Filament Stretching Flows with Strain-hardening Models and Sub-cell Approximations
H. Matallah, M.J. Banaai, K.S. Sujatha and M.F. Webster
This article analyses the transient viscoelastic response of strain-hardening fluids in
filament stretching flows. We utilise an Arbitrary Lagrangian/Eulerian temporal approach
(ALE), coupled with a particle-tracking procedure for free-surface movement and a hybrid
finite volume/element method upon the domain. We are able to contrast findings between
Oldroyd, Giesekus and linear Phan-Thien/Tanner models, and distinguish between single and
multi-mode implementations. In this manner, we identify the impact that greater severe strainhardening
has in this transient flow context. Contributions from shear-thinning rheology may
be gathered in particular by comparing single-mode solution response between a shearthinning
Giesekus and a constant shear viscosity Oldroyd-B model. A parameter study on
inertial and surface tension effects has been undertaken, where we isolate the occurrence of
asymmetries in the flow under certain conditions, leading to the onset and formulation of
bead-like structures. This elucidates the specific localised influence that surface tension and
gravitational forces have upon some stretching filament flows.
Report Titles
CSR 10-2005 A Network Model of Analogue Computation over Metric Algebras
John V. Tucker and Jeffery I. Zucker
We define a general concept of a network of analogue modules
connected by channels, processing data from a metric space A, and
operating with respect to a global continuous clock T. The inputs and
outputs of the network are continuous streams
u: T → A, and the
input-output behaviour of the network with system parameters from A
is modelled by a function Φ : C[T,A]p ×
Ar → C[T,A]q (p, q > 0, r ≥ 0),
where C[T,A] is the set of all continuous streams equipped with the
compact-open topology. We give an equational specification of the network,
and a semantics which involves solving a fixed point equation over
C[T,A] using a contraction principle. We analyse a case study involving a
mechanical system. Finally, we introduce a custom-made concrete computation
theory over C[T,A] and show that if the modules are concretely
computable then so is the function Φ.
Report Titles
CSR 11-2005 Newtonian mechanics and infinitely parallel computation
E.J. Beggs and J.V. Tucker
First, we reflect on computing sets and functions using measurements from experiments with a class of physical systems. We call this experimental computation. We outline a programme to analyse theoretically experimental computation in which a central problem is: Given a physical theory T, explore and classify the computational models that can be embedded in, and abstracted from, the physical systems specified by the physical theory T. We consider the embedding arbitrary sets, functions, programs, and computers into designs for systems that can be specified in subtheories or fragments T of Newtonian kinematics in order to explore some of the physical assumptions of T that allowed its systems to qualify as hyper-computers, i.e., physical models that compute sets and functions that cannot be computed in classical computability theory. In designing systems we work strictly within the chosen theory T and do not concern ourself with whether or not T is valid of the world today. We are interested in exploring the subtheory from a computational point of view and especially in restrictions on the assumptions of T that allow us to return from hyper-computation to classical computation.
Secondly, we give a construction of an infinitely parallel machine that can
decide all the arithmetical sets of natural numbers. We embed this hyper-computer as
system in 3-dimensions obeying the laws of a fragment of Newtonian kinematics. In
particular, the example shows that communication allowable in Newtonian kinematics is
especially powerful. We conclude with further reflections and open problems.
Report Titles
CSR 12-2005 The Rational Numbers as an Abstract Data Type
J.A. Bergstra and J.V. Tucker
We give an equational specification of the field operations on the rational
numbers under initial algebra semantics using just total functions and 12 equations.
A consequence of this specification is that 0-1 = 0, an interesting equation
consistent with the ring axioms and many properties of division. The existence of an
equational specification of the rationals without hidden functions was an open
question of L Moss. We give a thorough axiomatic analysis that uncovers some new axioms
for the divisibility operator and leads to equational specifications of some other algebras
of rationals, including one with the modulus function. We state some open problems,
including: Does there exist an equational specification of the field operations
on the rationals without hidden functions that is a complete term rewriting system?
Report Titles
CSR 13-2005 Interactive Multimedia Investigation of Experimental and Simulated Data Sets Using Dynamic Multi-Menus
I. Deliyannis and M.F. Webster
A detailed industrially-based multimedia case-study is considered, featuring experimental
and simulation dough-kneading data-sets. Multimedia environments and novel interaction techniques
are employed, creating flexible implemen-tations, whilst dealing with large and densely interrelated
data. Direct data-comparison across valid combinations is ac-tioned, through Multi-Menus.
Voiceover-streams and multiple navigation-paths are characteristic features. Multimedia
environment-level retiming supports synchronised presentation of non-uniform animations,
reducing re-rendering times. Through Multimedia environments, direct system-updates are practical,
whilst data-duplication is avoided. Such imple-mentation enhances the presentation impact-factor of
the work. As such, the system supports intelligent interrogation, that itself, may lead to heightened
awareness and meaningful interpretation of the data. This complicated interactive rheological
investigation, aided via Multimedia technology, spans across various parameter spaces.
These include geo-metric, fluid-type, speed, depth and stirrer-shape adjustments. Whilst the
resulting systems fulfil base-level presentation requirements over various media, the same systems
may be used for further data-evaluation
Report Titles
CSR 14-2005 Stabilised Computations for Viscoelastic Flows under Compressible Implementations
F. Belblidia, I.J. Keshtiban and M.F. Webster
We analyse and contrast different stabilisation methodologies embedded within a time-marching incremental pressure-correction
formulation. Numerical solutions are presented for an Oldroyd-B model under compressible implementations, considering flow through
a planar four-to-one abrupt-contraction. Various alternative stabilisation strategies and their combinations are analysed to hone the
response of the base hybrid finite element/volume implementation. To reflect the stabilised properties of each scheme, the study
interrogates levels of stable Weissenberg number (We) solution. Results indicate that most improvement has been encountered with a
Strain-Rate Stabilisation scheme, where critical We-levels have more than doubled above neutral variants, while stress peaks levels
have been constrained. Here, differed-correction characterises temporal error norm stress behaviour and the nature of the re-entrant
corner stress singularity. At a selected We-level and under a specific flow setting, all scheme variants have produced similar
salient-corner vortex behaviour, predicting vortex reduction under increasing We. In contrast, lip-vortex features are found to be
significantly affected by the particular re-entrant corner treatment applied. When present, lip vortices grow with increasing We.
Relaxation of the incompressible constraint points to important numerical anomalies, present under certain discretisations.
Report Titles
CSR 15-2005 Extensional response of the pom-pom model through planar contraction flows for branched polymer melts - PART 2
J. P. Aguayo, H. R. Tamaddon-Jahromi and M.F. Webster
One objective of this study is to assess the influence of the number of dangling arms at each end of the pom-pom molecule on flow characteristics
in a 4:1 planar rounded-corner contraction, where varying the number of arms affects the level of entanglement in the system.
For these complex flows, we evaluate the major influence of extensional viscosity and Trouton ratio
when comparing kinetic-based as opposed to phenomenological network-based models.
The stability of the proposed extended pom-pom model (XPP) is investigated for a range of Weissenberg numbers utilising a
hybrid finite-element/volume scheme. For this scheme, we solve the momentum-continuity equations by a fractional-staged
Taylor-Galerkin/pressure-correction procedure and invoke a cell-vertex
fluctuation-distribution finite volume scheme for the constitutive law.
Distinction may be drawn between fluid response in the extension-hardening regime and those displaying a degree of softening.
In particular, trends in salient-corner vortex-intensity response can be associated with the extensional properties of the
extended version of the pom-pom model. Critical levels of solution elasticity attainable
depend on precise extensional viscosity characteristics.
The influence of various model parameters upon field response is described
through rates of deformation, stress and stretch. This would include consideration
for parameters governing anisotropy (alpha), and the ratio of stretch to
orientation relaxation times (epsilon).
Report Titles
CSR 16-2005 Modelling Filament Stretching Flows with Strain-hardening Models and Sub-cell Approximations - Part II
H. Matallah, M.J. Banaai, K.S. Sujatha and M.F. Webster
This article analyses the transient viscoelastic response of strain-hardening fluids in filament stretching flows. We utilise an
Arbitrary Lagrangian/Eulerian temporal approach (ALE), coupled with a particle-tracking procedure for free-surface movement
and a hybrid finite volume/element method upon the domain. We are able to contrast findings between Oldroyd, Giesekus and linear
Phan-Thien/Tanner models, and distinguish between single and multi-mode implementations. In this manner, we identify the impact
that greater severe strain-hardening has in this transient flow context. Contributions from shear-thinning rheology may be gathered
in particular by comparing single-mode solution response between a shear-thinning Giesekus and a constant shear viscosity Oldroyd-B model.
A parameter study on body force and surface tension effects has been undertaken, where we isolate the occurrence of asymmetries in the flow
under certain conditions, leading to the onset and formulation of bead-like structures. This elucidates the specific localised influence
that surface tension and gravitational forces have upon some stretching filament flows.
Report Titles
CSR 17-2005 The SAT 2005 solver competition on random instances
Oliver Kullmann
An analysis of the SAT 2005 sub-competition on random instances is given.
This year the competition set-up was geared to establish a basic setting, focusing
on the instances near the (infamous) "50% densities", so first we have
to establish a more quantitative understanding of phase transitions here. We
present extended empirical results, clearly showing that the models used before,
which are motivated by large-scale considerations, are inadequate at the
relatively small scale considered here. Then the series and all individual instances
used in the competition are described. We give a formal definition of
the competition evaluation, and analyse the results of the competition, looking
into the details of the scoring mechanism as well as into alternative evaluation
methods.
Report Titles
Peter Mosses, John Power and Monika Seisenberger (Editors)
Selected Papers presented at the
CALCO Young Researchers Workshop
Swansea, Wales, September 2005
Report Titles
CSR 19-2005 Visual Signatures in Video Visualization
Min Chen, Ralf P. Botchen, Rudy R. Hashim, Daniel Weiskopf, Thomas Ertl and Ian Thornton
Video visualization is a computation process
that extracts meaningful information from original video
data sets and conveys the extracted information to users
in appropriate visual representations. This paper presents
a broad treatment of the subject, following a typical
research pipeline involving concept formulation, system
development, a path- nding user study and a eld trial
with real application data. In particular, we have conducted
a fundamental study on the visualization of motion
events in videos. We have, for the rst time, deployed ow
visualization techniques in video visualization. We have
compared the effectiveness of several different abstract
visual representations of videos. We have conducted a
user study to examine whether users are able to learn
to recognize visual signatures of motions, and to assist
in the evaluation of different visualization techniques.
We have applied our understanding and the developed
techniques to a set of application video clips. Our study has
demonstrated that video visualization is both technically
feasible and cost-effective. It provided the rst set of
evidence con rming that ordinary users can accustom to
the visual features depicted in video visualizations, and can
learn to recognize visual signatures of a variety of motion
events.
Report Titles