CSR 1-2002 Numerical prediction of extensional flows in contraction geometries: hybrid finite volume/element method
M. Aboubacar, H. Matallah, H.R.Tamaddon-Jahromi and M.F. Webster
We examine the flow of viscoelastic fluids with various shear and elongational properties
in axisymmetric and planar 4:1 contractions, under creeping flow conditions.
Particular attention is paid to the influence of elongational viscosity upon vortex
enhancement/inhibition. Simulations are performed with a new hybrid finite volume/
element algorithm. The momentum and continuity equations are solved by
a Taylor-Galerkin/pressure-correction finite element method, whilst the constitutive
equation is dealt with by a cell-vertex finite volume algorithm. Both abrupt
and rounded-corner configurations are considered. The Oldroyd-B fluid exhibits
vortex enhancement in axisymmetric flows, and vortex reduction in planar flows,
qualitatively reproducing experimental observation for some Boger fluids. For shearthinning
fluids (Phan-Thien/Tanner models), both vortex enhancement and inhibition
is observed. This follows trends in extensional viscosity. Lip-vortex activity
has been observed in planar and sharp-corner instances, but not in axisymmetric
or rounded-corner flows. Finally, cross-flow extensional-stress contours in the
salient-corner neighbourhood reflect the size and curvature of the associated vortex
structure.
Report Titles
CSR 2-2002 Modeling Free Surface Flows in Part-Filled Rotating Vessels: Vertical and Horizontal Orientationss
K.S.Sujatha and M. F. Webster*
This paper reports on the numerical simulation of rotating flows with free
surfaces, that arises in the food processing industry, namely in dough-kneading. Free
surface flow in a rotating cylinder is investigated when a fluid is stirred in a cylindrical
shaped vessel with a stirrer attached to the lid. The equations are solved in a threedimensional
cylindrical polar coordinate system. The numerical simulation is based on
a Taylor-Galerkin finite element formation, with an arbitrary Lagrangian-Eulerian
scheme to accommodate free-surface movement. Peeling and wetting conditions, that
depends on stretch-rate, are modeled to get the exact position of the surface. Freesurface
profiles are presented for different speeds of rotation and predictions compare
closely to equivalent experimental results. This is re-echoed through torque-time traces
for the part-filled situations, that demonstrate the distribution of torque and hence the
rate-of-work done, in the kneading process.
Report Titles
CSR 3-2002 Modelling and experimental studies of rotating flows in part-filled vessels: wetting and peeling
K.S.Sujatha, M.F.Webster, D.M.Binding and M.A. Couch
The main purpose of this paper is to corroborate numerical modeling and
experimental results for rotating flows with free-surfaces. This work is associated with
dough-kneading and the validation of surface positions. Free surface flow in a rotating
cylinder is investigated when a fluid is stirred in a cylindrical-shaped vessel with a
stirrer attached to the lid of the vessel. The stirrer may be placed in either concentric or
eccentric position with respect to the axis of the vessel. Both horizontal and vertical
orientations of the vessel are studied at various rotational speeds. Wetting and peeling
at solid boundaries is incorporated to achieve realistic simulations. Experimental
visualization for free-surfaces involve laser scatter technology and contemporary
imaging methods for more complex flows. A video capture technique is used to
determine peeling stresses experimentally, which compares well with the stress
obtained from numerical computations. Close agreement is obtained between
numerical and experimental flow fields and free surface profiles. Model fluids
employed are various percentage concentrations of CMC, which have shear-thinning
properties.
Report Titles
CSR 4-2002 Experimental and numerical simulation of dough kneading in filled geometries
D.M. Binding, M.A. Couch, K.S. Sujatha and M.F.Webster
The main objective of this study is to counterpart numerical model and experimental
studies for rotating flows associated with dough kneading, and validate the flow patterns
generated. The flows considered are in a complex domain setting. Two types of cylindrical
vessels are studied at various rotational speeds; one with one stirrer and a second with two.
Laser Doppler Anemometry is used to obtain the velocity vectors associated with the flow
fields. Close agreement is obtained between numerical and experimental flow fields and the
magnitudes of velocity vectors. Both sets of results show maximum shear-rates outside the
stirring rods. The rate-of-work done also peaks in this region and this is an important quantity
to dictate optimal mixer design.
Report Titles
CSR 5-2002 Transient Simulations for Nano-scale Filament Stretching with Large Deformation-Rates
K.S.Sujath and M.F. Webster
This article deals with the numerical simulation of filament stretching, on
the nano-scale and under very large deformation-rates. To compute transient
free-surface adjustment, a combination of mesh-stretching and fluid volume
conservation techniques have been applied. The field equations are solved
by a transient finite element algorithm, Taylor-Galerkin / pressure
correction.
Report Titles
CSR 6-2002 Contraction Flows of Highly-Elastic Liquids : Experiment and Simulation
K. Walters and M.F. Webster
It is well known that highly elastic liquids can exhibit
flow characteristics which are markedly different from
those found in Newtonian liquids. Nowhere is this
better seen than in the case of Contraction Flows,
whether axisymmetric or planar.
A phenomenon of 'vortex enhancement', where the
corner vortex (which is present in Newtonian liquids)
increases in size, often in an extravagant manner.
Whether the enhancement is due to the growth of the
salient corner (Newtonian) vortex or results from the
appearance and ultimate domination of a so called 'lip
vortex' is a very provocative question
which has yet to be fully understood.
In the present paper, we first highlight what is
already known experimentally about the flow of
highly-elastic liquids in a contraction. We then
discuss the distinctive challenges encountered in the
numerical simulation of these flows, focusing on
recent attempts within the University of Wales
Institute of non-Newtonian Fluid Mechanics to predict
and understand the experimental observations. We
limit the discussion to polymer solutions, where the
viscoelastic phenomena are so apparent. We
consider both shear-thinning solutions and also
constant-viscosity Boger fluids, flowing in planar and
axisymmetric contractions.
Report Titles
CSR 7-2002 The Modeling of Dough Mixing with Free Surfaces in Two and Three dimensions
M.F. Webster, D. Ding and K.S. Sujatha
This paper reports work on the two and three-dimensional numerical simulation of dough
mixing with free surfaces, that arises in the food processing industry. Free surface flow in
a rotating cylinder is investigated when a fluid is mixed in a cylinder with a stirrer.
Different dough mixer designs are investigated. The rotating stirrer may be placed either
in a concentric or eccentric arrangement with respect to the axis of the vessel being
horizontal or vertical. The equations are solved in a three dimensional cylindrical polar
coordinate system. The numerical simulation is based on a Taylor-Galerkin finite element
formation, with an arbitrary Lagrangian-Eulerian scheme to accommodate free surface
movement. Predictions compare closely to equivalent experimental results.
Report Titles
CSR 8-2002 Towards a Document Centred Computer-Aided Control System Design Environment
Al Sadiq ul Amin M. Madani Halepota, Christopher P. Jobling and Philip W. Grant
Most conventional design processes produce documentation as a by-product: design
is done within an environment or collection of tools and the design outputs, models,
diagrams, results, etc are gathered together along with commentary (usually with hindsight)
into some kind of document at the end of the process. Inspired by ideas taken from literate
programming and notebook interfaces to design tools, a prototype document centred design
document has been developed. In such an environment, the document is the main product and
the design is a by-product of documenting the design. By implementing the framework components
of the system in Java and by using the extended markup language (XML) to encode
the contents of the documents, the system is made platform neutral and therefore portable. An
example document centred environment for computer-aided control system design (CACSD),
that integrates MATLAB and SIMULINK with the document-based framework, is briefly described
and indications for future possibilities for this technology are given.
Report Titles
CSR 9-2002 Modelling Three-Dimensional Rotating Flows in Cylindrical-Shaped Vessels
K.S. Sujatha and M.F. Webster
This paper reports on a study concerned with the numerical simulation of
dough kneading that arises in the food processing industry. The
flows considered
are in a complex domain setting. Two dough mixers running at various
rotation speeds are studied; one with a single stirrer, the other with two stirrers.
Stirrers are fixed on the lid of the vessel and the motion is driven by the rotation
of the outer vessel. Two different mixer orientations are considered, generating
horizontal or vertical-rotating
ow fields. Three-dimensional numerical simulations
are performed on the full
ow equations in a cylindrical polar co-ordinates
system, through a finite-element, semi-implicit time stepping, Taylor-Galerkin
pressure-correction scheme. The results re
ect excellent agreement against the
equivalent experimental findings. The motivation for this work is to develop advanced
technology to model the kneading of dough. The ultimate target is to
predict and adjust the design of dough mixers, so that optimal dough processing
may be achieved notably, with reference to local rate-of-work input.
Report Titles
CSR 10-2002 Distributed Parallel Computation with Multi-mode Viscoelastic models of Wire-Coating Flows
H. Matallah, A. Baloch and M.F. Webster
Wire-coating flow is simulated, involving polymer melt coatings and tube-tooling process
design. A finite element method is employed, based on a semi-implicit time-stepping
Taylor-Galerkin/pressure-correction scheme. The exponential Phan-Thien/Tanner model
is used in its multi-mode form to represent a high-density polyethelyne (HDPE) polymer.
Both shear-thinning and elongation-softening properties are represented. Solutions are
generated through sequential and parallel modes of computation, over a homogeneous
network cluster of Intel workstations running Solaris and Parallel Virtual Machine (PVM).
Parallel results are compared against those obtained on a single processor (sequential).
Linear speed-up is observed with the number of processors.
Report Titles
CSR 11-2002 Time-Dependent Algorithms for Viscoelastic Flow - finite volume/element schemes
H.R. Tamaddon-Jahromi, M. Aboubacar, H. Matallah and M.F. Webster
Hybrid finite volume/element methods are investigated within the context of transient viscoelastic
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 diffculties are highlighted. A new
method emerges, with the Low Diffusion B (LDB, with or without mass-matrix iteration) as
the optimal choice.
Report Titles
CSR 12-2002 Viscoelastic Computations of Polymeric Wire-coating Flows
H. Matallah, P. Townsend and M.F. Webster
This study considers both a single and multi-mode viscoelastic analysis for wirecoating
flows. The numerical simulations utilise a finite element time-stepping technique,
a Taylor-Petrov-Galerkin/pressure-correction scheme employing both coupled and decoupled
procedures between stress and kinematic fields. An exponential Phan-Thien/Tanner
model is used to predict pressure-drop and residual stress for this process. Rheometrical
data fitting is performed for steady shear and pure extensional flows, considering
both high and low density polyethylene melts. Simulations are conducted to match experimental
pressure-drop/flowrate data for a contraction flow. Then, for a complex industrial
wire-coating flow, stress and pressure drop are predicted numerically and quantified. The
benefits are extolled of the use of a multi-mode model that can incorporate a wide-range
discrete relaxation spectrum to represent flow response in complex settings. Contrast
is made between LDPE and HDPE polymers, and dependency on individual relaxation
modes is identified in its contribution to overall flow behaviour. (This is
a revised version of report CSR 10-2000)
Report Titles
CSR 13-2002 Multimedia environments and interactive scientific presentation of industrially-based data sets
I. Deliyannis and M.F. Webster
A multimedia framework is employed, to embrace the interactive and
visual presentation of a series of case-studies with large conventional (static),
and multi-mode (dynamic) data sets. This reveals multifaceted presentation
requirements. Graphs are utilised to enable rigorous MMS design, effortless
updates and unproblematic future expansion. Multimedia environments (MME)
facilitate rapid prototyping and a data-oriented approach is advocated. As a
result, the customised presentation attributes vary widely from case-study to
case-study, touching upon aspects such as interfaces, interaction, data content
organisation and presentation styles. At the user-level, a number of novel
features are introduced, beyond those frequently observed in propriety software.
Interaction through multi-menus engenders direct interfacing with the
underlying graph, enabling effortless transition, and direct data-access,
notwithstanding remote data content. Combinations of novel interaction
techniques are realised, being combined under a single interface. The
presentation content, originates from simulation and experimental scientific
fields of study. The MMSs advanced have been actively used to cover
presentation requirements, in addressing both industrial and academic
audiences.
Report Titles
CSR 14-2002 Refined Program Extraction From Classical Proofs
Ulrich Berger, Wilfried Buchholz, Helmut Schwichtenberg
The paper refines the well-known method of extracting programs from
non-construction proofs via Friedman's A-translation. Several
examples show that the refined method yields shorter and more efficient
programs.
Report Titles
CSR 15-2002 Term rewriting for normalization by evaluation
Ulrich Berger, Matthias Eberl and Helmut Schwichtenberg
We extend normalization by evaluation from the pure typed
lambda-calculus
to general higher type term rewriting systems. We distinguish between
computational rules and proper rewrite rules, and define a domain
theoretic model intended to explain why normalization by evaluation
for the former is much more efficient. Normalization by evaluation is
proved to be correct w.r.t. this model and w.r.t. call-by-name
reduction.
Report Titles
CSR 16-2002 Minimisation vs. recursion on the partial continuous functionals
Ulrich Berger
We study the relationship between minimisation and recursion
on the partial continuous functionals of finite types.
We prove that already at type level two minimisation is weaker than
recursion.
Report Titles
CSR 17-2002 Program extraction from Gentzen's proof of transfinite induction up to epsilon_0
Ulrich Berger
We discuss higher type constructions inherent to intuitionistic
proofs. As an example we consider Gentzen's proof of transfinite
induction up to the ordinal epsilon_0. From the constructive content
of this proof we derive higher type algorithms for some ordinal
recursive hierarchies of number theoretic functions as well as simple
higher type primitive recursive definitions of tree ordinals of all
heights < epsilon_0.
Report Titles
CSR 18-2002 Modified Bar Recursion and classical dependent choice
Ulrich Berger and Paulo Oliva
We introduce a variant of Spector's Bar Recursion in finite types to
give a realizability interpretation of the classical axiom of
dependent choice allowing for the extraction of witnesses from proofs
of Sigma_1 formulas in classical analysis. We also give a bar
recursive definition of the fan functional and study the relationship
of our variant of Bar Recursion with others.
Report Titles
CSR 19-2002 First report on an adaptive density based branching rule for DLL-like SAT solvers, using a database for mixed random conjunctive normal forms created using the Advanced Encryption Standard (AES)
Oliver Kullmann
We introduce an adaptive density-based heuristics hA for a given (DLL-
like, otherwise arbitrary) SAT solver A, leading to a (hopefully) improved
SAT solver A0. The determination of hA is motivated by a generalised
threshold conjecture for random formulas, and exploits a database for satisfiability and
hardness of random formulas. To build up such a (large)
database, a new reliable pseudo-random formula generator OKgenerator,
based on AES (Advanced Encryption Standard), the successor of DES, is
introduced.
Report Titles
CSR 20-2002 Multi-Level Modelling and Interactive Multimedia presentation of Scientific Data over various Media
I. Deliyannis and M.F. Webster
Multimedia environments are utilised to construct interfaces, comprising of advanced interactive features. This
involves the organisation and presentation of complex Computational Fluid Dynamics and experimental data
(multimedia streams and static instances) for industrial case-studies. Modular interface constructs are employed
to enable rapid and sound system-development, utilising object-oriented practices, based on an underlying
graph structure. The multimedia nature of the implementation enables interaction with synchronised animated
flow-visualisation data (Motion-blur, static plots animated through settings, solid-modelling animations),
which, in turn, is intended to enhance the understanding of the underlying flow processes. The resulting
implementation can be ported to various computer-platforms, or streamed over Internet connections without
compromise in quality. It is shown how distinct individual multimedia implementations are constructed,
through a range of industrially-based and educational case-studies. In addition, it is discussed how a set of
such multimedia systems can be merged into a single environment, and linked externally, locally (single computer),
or over Internet communication channels.
Report Titles
CSR 21-2002 General Purpose Exact Real Arithmetic
J. Blanck
Implementation techniques for exact computations are described
and to some degree evaluated. In particular, two basic algorithms for
exact compuattions are identified and investigated. The very important
choice of approximations is examined, inparticular for the space
of the reals. The proposed approximations contain an error term and
it is argued that the error term should be variable, but bounded.
Report Titles
CSR 22-2002 Numerical Simulation of Viscous Filament Stretching Flows
M.S. Chandio, H. Matallah and M.F. Webster
A numerical study of the stretching of a Newtonian fluid filament is analysed.
Stretching is performed between two retracting plates, moving under constant
extension rate. A semi-implicit Taylor-Galerkin/pressure-correction finite element
formulation is employed on variable-structure triangular meshes. Stability and
accuracy of the scheme is maintained up to larger Hencky strain-levels. A nonuniform
radius profile, minimum at the filament mid-plane, is observed along the
filament-length at all times. We have found maintenance of a suitable mesh-aspect
ratio around the mid-plane region (maximum stretch zone) to restrict early filament
break-up and consequently solution divergence. As such, true transient flow
evolution is traced and the numerical results bear close agreement with the literature.
Report Titles
CSR 23-2002 Investigating the behaviour of a SAT solver on random formulas
Oliver Kullmann
We introduce an adaptive density-based heuristics for a given SAT
solver, using the knowledge built into the solver and improving upon it.
The computation of the heuristics uses approximations of the satisfiability
probability and of the average conditional running times on satisfiable
and unsatisfiable inputs for the given domain of problems, where the underlying
probability spaces are implicitly defined using a control parameter.
Using relative densities and the number of variables together as
control parameter, we arrive at the natural generalisation of the constant
clause-length random formula model, where now different clause-lengths
are possible.
In order to guide computations of the above approximations we introduce
and argue in favour of three conjectures. Conjecture (TL) about
the thermodynamical limit for random formulas guarantees the existence
of thresholds in a very general sense. Considering only unsatisfiable formulas,
Conjecture (URE) states that resolution complexity is exponential
with high probability for all (mixed clause-length) densities. Considering
satisfiable together with unsatisfiable formulas and measuring resolution
complexity of satisfiable formulas as infinite, this weakened Conjecture
(URE) follows from recent resolution lower bounds of Beame et al. Our
third conjecture (DUSE) now assures, that the influence of the exponential
running time on unsatisfiable formulas for DLL-like algorithms guaranteed
by (URE) is in fact negligible in satisfiability density regions, by
saying that the decay of the probability of finding unsatisfiable formulas
in satisfiability regions is always super-exponential. It seems also, that the
influence of satisfiable formulas in unsatisfiability regions is negligible.
As approximation technique for (generalised) satisfiability probabilities
we formulate an abstract (simplifying) framework for finite size scaling
techniques, and discuss techniques for experimental determination of
thresholds, critical exponents and scaling functions. These considerations
are then applied to satisfiability of 3-CNF's by (repeated) elimination of
pure literals, and to the (absolute) satisfiability of 3-CNF's.
As a case study for the approximation of average conditional running
times, we consider the SAT solver OKsolver on random 3-CNF. We arrive
at a global model for the running times on unsatisfiable formulas (for all
densities), while for satisfiable formulas additional to the phase transition
w.r.t. pure literals (at density ~ 1.64) we observe a phase transition at
density ~ 3.07 from never finding a failed literal to always finding one,
while at density ~ 3.26 (determined by Achlioptas as the maximal density
where myopic SAT algorithms can succeed) a phase transition from
an always backtrack-free search tree to a search tree always including
backtracking takes place. Above density 3.26 we find super-polynomial
running time of OKsolver (while below the running time is polynomial).
The experimental framework is given by the new pseudo-random formula
generator OKgenerator, based on AES (Advanced Encryption Standard,
the successor of DES), an XML standard for communication about SAT
results, and a relational database for random formulas.
Report Titles
CSR 24-2002 WWW Delivery of Graph-based, Multi-level Multimedia Systems: Interaction Over Scientific, Industrial and Educational Data
M.F. Webster and I. Deliyannis
Many present-day multimedia presentation systems utilise technologies such as JAVA applets/scripts, ASP, JSP, XML,
employed to cover advanced multi-level presentation requirements. These often suffer from technology-imposed
disadvantages, an example being the lack of content re-use in WWW settings. The development of a diverse range of
interactive educational, scientific and industrially-based multimedia systems is described in this paper. The goal is to
deliver comprehensive multimedia-system functionality over the WWW, using a single multi-purpose implementation,
and minimising the need for additional web-development work. Synchronisation of multiple data-types need to be
embraced, that include animations (here featuring simulation and experimental data), sound-streams (voice-over,
music), static images, and text fields. This rich data-domain addresses research-data, educational and public-awareness
content-levels. Each multimedia-system utilises a unique structure, described through a navigational-graph. This
facilitates multiple, interactive modes within a single implementation instance. Multimedia environments are utilised,
featuring such desirable characteristics as remote data-access, dynamic stream-handling and manipulation algorithms,
and case-based dynamically-adjustable interaction and frame-linking through conditional high-level scripting.
Multimedia-system linking is processed to create a higher-order master, multimedia system, encapsulating transition
between like-minded thematic multimedia systems.
Report Titles
CSR 25-2002 Transient Start-up of Plane Poiseuille Flow
M Aboubacar, T N Phillips, HTJ Tammadon-Jahromi, B Snigerev and MF Webster
This article investigates various improvements to two existing
finite volume (fv) algorithms, specifically constructed to address viscoelastic flows.
Here, we consider model problems to identify fundamental algorithmic advances.
Two alternative fv-approaches are advocated and contrasted for their properties, a
hybrid cell-vertex scheme and a cell-centred staggered-grid scheme. The former utilises
fe-discretisation for momentum/continuity components and fv for constitutive equations.
The cell-centred scheme is a pure fv-discretisation. Both schemes adopt a
time-stepping solution approach.
The model problem selected for study is that of the transient start-up flow of an
Oldroyd-B model fluid in a channel. This is a pure shear transient flow, so that
inertia is unimportant. Here, one may solve for the transient evolution of velocity
and/or stress, and compare results against the analytical solution available.
For the cell-vertex scheme, we solve in a coupled velocity/stress sense, and consider
variation in fluctuation distribution schemes (upwinding), different combinations of
'flux' and 'median-dual-cell' spatial discretisations and time-term treatments.
Unstructured and structured meshes may be used, based largely on triangular griding.
The focus lies with establishing optimal accuracy and temporal stability, within the
framework offered. Such a cell-vertex scheme has been established as second-order
accurate for steady model problems. The new dimension here is time-accuracy.
For the cell-centred scheme, improved methodology on area-weighting is considered
attracting higher-orders of accuracy within a semi-Lagrangian implementation. This
scheme has already been established within the context of model problems and some
complex flows, whilst utilising first-order area weighting for backtracking along
the solution characteristics in time.
Report Titles
CSR 26-2002 Numerical Simulation of Contraction Flows for Boger Fluids using Finite Volume Methods
M Aboubacar, T N Phillips, HTJ Tammadon-Jahromi, MF Webster and A J Williams
Simulation of viscoelastic flows is undertaken, considering single-mode differential
models and two different numerical schemes. There is interest in constant viscosity
memory fluids and their representation of flow structures and characteristics, such as
vortex behaviour, development of stress boundary layers, and pressure drop estimation.
We address such issues through increasing flow rate for a given fluid. To this end we
consider high and low solvent fractions for Oldroyd models to approximate Boger fluids.
Elsewhere, constant viscosity and shear-thinning models have been investigated in
inertialess flows, whilst increasing relaxation time of the fluid in question.
Flows under consideration include both planar and axisymmetric contraction flows.
The geometric ratio adopted is restricted to the common 4:1 case. A series of meshes
are tested, covering triangular unstructured and rectangular structured forms.
Numerical techniques employed are time-stepping algorithms, one of hybrid finite
element/volume type, the other of pure finite volume form. In the former, a
Taylor-Galerkin/pressure-correction finite element discretisation is used to
solve for continuity and momentum balance equations, in combination with a
second-order cell-vertex scheme for stress. Such a scheme has been developed for
triangles, that appeals to both fluctuation distribution and median-dual-cell nodal
update contributions.
The pure finite volume scheme is a staggered-grid cell centred scheme, applied on
rectangles, depending upon a semi-Lagrangian formulation. In this formulation
the convection terms are treated in a semi-Lagrangian fashion, which has the effect of
stabilising the calculations. The system of algebraic equations at each time step are
solved using the SIMPLER methodology.
A comparison of the two approaches will be presented showing the development of flow
structures and characteristics with increasing Weissenberg number. Comments will also
be made about comparisons against experimental observations.
Report Titles
CSR 27-2002 Image-Swept Volumes
Andrew S. Winter and Min Chen
Many graphical objects can be represented by swept volumes (including its subset Ð generalised cylinders)
by sweeping 2D or 3D templates along 3D trajectories. In this paper, we present a new approach for constructing
swept volumes using image templates. We utilise scalar fields as our underlying data type, and
employ volume ray casting techniques for rendering swept volumes in their original sweeping specifications
as well as in their voxelised approximations. In addition to some simple image-swept volumes, we also treat
multi-channel image templates, video templates, generalised sweeps, and self-intersecting trajectories. This
approach enables us to model swept volumes with heterogeneous interiors and amorphous effects. It also facilitates
the use of constructive volume geometry for creating complex scenes in both modelling and rendering space.
Report Titles
CSR 28-2002 Comparative Evaluation of Visualization and Experimental Results Using Image Comparison Metrics
Hualin Zhou, Min Chen and Mike F. Webster
Comparative evaluation of visualization and experiment results is
a critical step in computational steering. In this paper, we present
a study of image comparison metrics for quantifying the magnitude
of difference between a visualization of a computer simulation
and a photographic image captured from an experiment. We examined
eleven metrics, including three spatial domain, four spatialfrequency
domain and four HVS (human-vision system) metrics.
Among these metrics, a spatial-frequency domain metric called
2nd-order Fourier comparison was proposed specifically for this
work. Our study consisted of two stages: base cases and field
trials. The former is a general study on a controlled comparison
space using purposely selected data, and the latter involves imagery
results from computational fluid dynamics and a rheological experiment.
This study has introduced a methodological framework for
analyzing image-level methods used in comparative visualization.
For the eleven metrics considered, it has offered a set of informative
indicators as to the strengths and weaknesses of each metric. In
particular, we have identified three image comparison metrics that
are effective in separating ÒsimilarÓ and ÒdifferentÓ image groups.
Our 2nd-order Fourier comparison metric has compared favorably
with others in two of the three tests, and has shown its potential to
be used for steering computer simulation quantitatively.
Report Titles
CSR 29-2002 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. 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 di¨erential 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 fluids 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 30-2002 Time-dependent algorithms for viscoelastic flow: bridge between finite-volume and finite-element methodology
M. Aboubacar, H.R.Tamaddon-Jahrom and M.F. Webster
This article considers transient, planar Poiseuille flows for viscoelastic fluids. We propose a
novel time-dependent hybrid finite volume (fv)/finite element (fe) algorithm. This approach
combines a Taylor-Galerkin fe-treatment for mass and momentum conservation equations, with
a cell-vertex fv-discretisation of the hyperbolic stress constitutive equation. A consistent formulation
for the constitutive equation is key. This incorporates fe and fv-treatment of the
various terms. In this manner, an accurate transient algorithm emerges, which reproduces analytical
solution structure, both in core-flow and across shear-boundary zones.
Report Titles
CSR 31-2002 Multimedia presentation and interactive interrogation of Reverse Roller-Coating data
I. Deliyannis, J. Harvey and M. F. Webster
Interactive investigation of an industrial case-study is addressed, through the
utilisation of multimedia presentation technology. A principal aim is to evaluate
results through interactive interrogation, covering industrial requirements to
identify optimal operating windows through parameter adjustment. Both steady
and transient simulated flow-states are evaluated. The data is interpreted,
utilising the MMS to navigate through the large data-set involved. Flow settings
and results are discussed, whilst innovative presentation techniques are described
and implemented through multimedia environments. World-wide-web delivery,
streaming, underlying graphs, data-compression, voiceover and availability of
cruise-control navigation, are multimedia-related features that can render the
current system accessible to wide audiences over the internet. The generality of
presentation methods classifies this case-study as a characteristic example, to be
adopted for alternative data-sets.
Report Titles
CSR 32-2002 Computation of Viscoelastic Flows with Embedded Recovery Schemes
H. Matallah, P. Townsend and M.F. Webster
We analyse dfferent types of embedded recovery techniques for primary and secondary finite
element field variables in applications involving viscoelastic flows. For the primary stress variables
of an Oldroyd-B model, a direct/local averaging method and a patch recovery technique
are compared. For velocity gradient recovery, local direct methods are compared to Galerkin
least squares methods. Superconvergence properties are intrinsic to the methodology. Flow
problems addressed include a sink flow, start-up channel flow and flow past a sphere. Such
benchmark test problems are employed effectively to identify the properties of these various
recovery techniques. We examine their comparative influence upon accuracy and stability of a
semi-implicit Taylor-Galerkin/pressure correction scheme.
Report Titles
CSR 33-2002 A Multimedia Investigation Environment for Rheological Contraction- Flow data-sets
I. Deliyannis and M.F. Webster
The Contraction-Flows multimedia system
(MMS) focuses on rheological studies. It involves planar
and axisymmetric data, for four different geometries, and
five model-viscoelastic fluids, across the maximum obtainable
ranges of fluid-elasticity. Overall, optimal processing
windows are sought, across material systems,
process design and operating conditions, through simulation
and visualisation. This is brought together and exemplified
under the present MMS. Principal aspects of
this integrated data-evaluation implementation include:
"user-defined data categorisation and presentation", "effortless
navigation", "comparison across multiple modes"
and "direct access to inter-related data, on-demand". Factors
that have enabled the straightforward implementation
include, the uniformity of data and the extensive use of
object-technology to minimise re-programming requirements.
As a consequence, these factors did not impose
additional time-development constraints, when taking
under account the increased complexity of implementation.
Report Titles
CSR 34-2002 Efficient Exact Computation of Iterated Maps
J. Blank
It is possible to effectively compute the forward obit of iterated maps
contrary to often held beliefs that rounding errors and sensitivity on
inputs make this impossible. However, exact real arithmetic can compute the
forward orbit of the logistic map and many other maps using linear space
resources and O(nlog n M(n)) time, where M(n) is the time it takes to
multiply two numbers of n bits, and n is the number of iterations computed.
Some insights into implementation issues of exact real arithmetic is
arrived at, and tested successfully in actual computations. In particular,
it is found that bottom-up propogation of error terms is likely to be
preferable in involved computations. This will allow for exact real
computations that run within some constant factor of the time for the
corresponding floating point computation when the computation is stable.
Moreover, the exact real computation correctly handles unstable
computations and delivers a correct answer using time and space resources.
Report Titles