CSR 1-2001 Effectivity of Regular Spaces
J. Blank
General methods of investigating effectivity on regular Hausdorff (T3) spaces is considered. It is shown that there exists a functor
from a category of T3 spaces into a category of domain representations.
Using this functor one may look at the subcategory of effective domain
representations to get an effectivity theory for T3 spaces. However, this
approach seems to be beset by some problems. Instead, a new approach
to introducing effectivity to T3 spaces is given. The construction uses
effective retractions on effective Scott-Ershov domains. The benefit of
the approach is that the numbering of the basis and the numbering of
the elements are derived at once.
Report Titles
CSR 2-2001 Emergent Restructuring of Resources in Ant Colonies: A Distributed Approach to Real World Engineering Problems
A.E. Langham and P.W. Grant
In this article two engineering problems are solved using colonies of artificial ant-like
agents. These agents must restructure the resources in their environment in a manner which
corresponds to a good solution of the underlying problem. The application areas considered
are employed in parallel simulations of solutions of partial differential equations using
the Finite Element Method. The problem domain is first discretised into a set of
geometrical elements and solution for quantities such as material strain or pressure is
computed at the element nodes. For parallel execution, the mesh is
partitioned into submeshes so that the work
can be scheduled equally amongst processors
with the communication kept to a minimum. Communication occurs when two connected nodes
are assigned to different processors. Standard approaches to these
problems use recursive methods in which the final solution is dependent on
solutions found at higher levels. For example partitioning into k sets
is done using recursive bisection and meshing is often performed by
creating an initial coarse-grained mesh and inserting extra nodes into
the existing elements to achieve the required density. The inherently
parallel, distributed nature of the swarm-based paradigm allows us to
simultaneously partition into k sets or create different parts of the
mesh at the same time. Furthermore, because this approach is dependent
only on the state of the local environment it is ideal for problems of an
adaptive nature which are difficult for standard approaches to tackle.
Results show that this approach can be superior in quality when compared to
standard methods. However, it is not as efficient and hence we outline
various measures to both speed up and improve the quality of the methods
presented.
Report Titles
CSR 3-2001 JACIE - an Authoring Language for the Rapid Prototyping of Collaborative Applications
Abdul S. Haji-Ismail, Min Chen, Philip W. Grant and Mark Kiddell
With the World Wide Web (WWW) becoming the de facto standard
for human-computer interaction and human-human communication, there
is a need to develop net-centric, multimedia and collaborative
applications. We introduce a new scripting language,
JACIE, designed to support rapid prototyping and implementation
of such applications. The necessity to
support the management of multimedia interaction and communication in
collaborative applications is highlighted. JACIE
facilitates such support through the concepts of channels and a
collection of interaction protocols. JACIE also features a
template-based programming style, a single program for both client and
server, and platform-independence by using Java as the target language.
All these features characterise a desirable collaborative software
engineering tool.
Report Titles
CSR 4-2001 Parallel Computation of Two-Dimensional Rotational Flows of Viscoelastic Fluids in Cylindrical Vessels
A. Baloch, P.W. Grant and M.F. Webster
The numerical simulation of two-dimensional
incompressible complex flows of viscoelastic fluids is presented. The
context is one, relevant to the food industry, of mixing within a
cylindrical vessel, where stirrers are located on the lid of the
vessel. Here, the motion is considered as driven by the rotation of
the outer vessel wall, with various stirrer locations. With a single
stirrer, both a concentric and an eccentric configuration are adopted.
A further eccentric case with two stirrers is also contrasted against
the above, where a symmetrical arrangement is assumed. The parallel
numerical method adopted is based on a finite element semi-implicit
time-stepping Taylor-Galerkin/pressure-correction scheme, posed in a
cylindrical polar coordinate system. Initially, flows are realised
for Newtonian fluids. For viscoelastic fluids, constant viscosity
Oldroyd-B and two shear-thinning Phan-Thien/Tanner constitutive models
are employed. Both linear and exponential models
at two different material parameters are considered. This permits a
comparison of various shear and extensional properties and their
respective influences upon the flow fields generated. Variation with
increasing speed of vessel and change in mixer geometry are analysed,
with respect to the flow kinematics and stress fields produced.
Simulations are conducted via distributed parallel processing,
performed on a cluster of work-stations, employing a conventional
message passing protocol (PVM). Parallel
results are compared against those obtained on a single processor
(sequential). Ideal linear speed-up with the number of processors is
observed.
Report Titles
CSR 5-2001 Finite Element Distributed Computation for Viscoelastic Rotating Flows
A. Baloch, P.W. Grant and M.F. Webster
This paper is concerned with the parallel computation of incompressible viscoelastic rotating flows. Such flows arise in many industrial settings being particularly important in the food industries, for materials such as dough. Here, the material is driven by one or two stirrers, rotating about the centre of a cylindrical vessel, fixed to a lid. The stirrers may be positioned in eccentric arrangement with respect to the axis of the vessel. The motivation for this work is to advance fundamental technology modelling the kneading of dough with the ultimate aim to predict the optimal design of dough mixers themselves, hence, leading to efficient dough processing.
The numerical method employed is a time-marching semi-implicit Parallel-Taylor-Galerkin scheme, posed in a cylindrical polar coordinate system. This scheme is second-order in time and based on a fractional-staged pressure-correction formulation.
Parallel computations are performed, via domain decomposition,
on homogeneous and heterogeneous
distributed networks using the Parallel Virtual Machine
message passing protocol. Parallel timings are compared
against those for sequential computation. Ideal
linear speed-up is observed with increasing numbers of processors.
This is achieved through a sophisticated implementation that effectively
masks communication within pure computation costs.
Report Titles
CSR 6-2001 Finite Element Distributed Computation for Viscoelastic Rotating Flows
K Walters and M.F. Webster
In this general lecture, we shall first outline the way computational non-Newtonian fluid mechanics differs from conventional CFD. We do this by briefly outlining the major historical developments in this relatively new field of science, which is conveniently called Computational Rheology. To illustrate essential features, we limit the discussion to the Oldroyd B, UCM and Phan-Thien/Tanner constitutive models.
In order to provide a serious challenge to existing numerical codes, we describe some recent unpublished experimental results on ow through a contraction of constant-viscosity
(Boger) and also shear-thinning elastic liquids. Both planar and axisymmetric contractions are of interest, and pressure drops and observed ow structures provide the relevant
points of contact between experiment and numerical production.
Numerical codes, developed at UWS involving a hybrid finite element/finite volume
scheme for Oldroyd B and Phan-Thien/Tanner constitutive models, are applied to the
contraction-flow problems and an encouraging agreement is demonstrated between theory
and experiment. Specifically, the dramatic experimental differences between
flow in
planar and axisymmetric contractions and between constant-viscosity and shear-thinning
polymer solutions are mirrored in the numerical predictions, at least in a qualitative sense.
Notwithstanding these encouraging developments, the review ends with a realistic
assessment of the challenges still awaiting computational rheologists, with particular
reference to the choice of constitutive model and the possibility of further
refinements to the numerical techniques.
Report Titles
CSR 7-2001 Modelling Three-Dimensional Mixing Flows in Cylindrical-Shaped Vessels
K.S. Sujatha, D. Ding and and M.F. Webster
This paper reports on a study concerned with the numerical simulation of
dough mixing that arises in the food processing industry. The flows considered are in a
complex domain setting. Two dough mixers at various rotation speeds are studied; one with
one stirrer and the other with two stirrers. Numerical simulations are based on three
dimensions in the cylindrical polar co-ordinates system. The results reflect close agreement
with the equivalent experimental results. The motivation for this work is to develop and
advance technology to model the mixing 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 work input on the dough.
Report Titles
CSR 8-2001 Numerical simulation for reverse roller-coating with free-surfaces
M.S.Chandio and M.F.Webster
This article is concerned with the numerical simulation of a reverse roller-coating
process, which involves the computation of Newtonian viscous incompressible flows with
free-surfaces. A numerical scheme is applied of a transient finite element form, a semi-implicit
Taylor-Galerkin/pressure-correction algorithm. For free-surface prediction, we use
kinematic boundary adjustment with a mesh-stretching algorithm. In the present work, an
alloy sheet (foil) passes over a large roller and then a smaller applicator roller, which provides
the in-feed. In combination, the applicator roller, the foil and the fluid form part of the
underside coating mechanism. The aim of this study is to investigate fundamental aspects of
the process, to ultimately address typical coating instabilities. These may take the form of
chatter and starvation. A uniform coating thickness is the desired objective. A mathematical
model is derived to describe the solvent coating applied to the underside of the sheet,
assuming that the lacquer is a Newtonian fluid. In particular, the work has concentrated on the
flow patterns that result and a parameter sensitivity analysis covering the appropriate
operating windows of applied conditions. Effects of independent variation in roll-speed and
foil-speed are investigated, to find that maxima in pressure, lift and drag arise at the nip and
are influenced in a linear fashion. These quantities decrease linearly with increasing roll-speed,
and increase linearly with increasing foil-speed.
Report Titles
CSR 9-2001 Stabilisation Techniques for Viscoelastic Flows
H. Matallah, P. Nithiarasu and M.F. Webster
In a comparative study, three di erent procedures of stabilisation techniques
are considered for incompressible viscoelastic ow. The standard benchmark of ow past
a sphere falling in a cylindrical vessel is employed to test these stabilisation techniques.
First, discontinuity capturing (for stress) has been employed to investigate stabilisation
properties. Then, the Zienkiewicz - Zhu (ZPR-Q) quadratic patch recovery (for velocity
gradients) is analysed and compared with a direct recovery technique. Finally, a third
procedure is based on strain-rate stabilisation (for momentum). Results demonstrate that
discontinuity capturing itself yields reasonable stabilisation properties, and quadratic patch
recovery improves the solution somewhat over the linear version, but is not as stable as
direct averaging. Strain-rate stabilisation also provides enhanced stabilisation properties
comparable to those of discontinuity capturing.
Report Titles
CSR 10-2001 On the Treatment of Source Terms in Cell-Vertex Finite Volume fluctuation-Distribution Schemes For Viscoelastic Flow
M.S. Chandio and M.F. Webster
The accuracy, stability and consistency of a new cell-vertex hybrid nite element/volume
scheme is investigated in the numerical solution of a model viscoelastic sink ow. Here, the
interest is to explore the consequences of utilising conventional cell-vertex methodology for
an Oldroyd-B model and to demonstrate resulting drawbacks in the presence of complex source
terms. Alternative strategies worthy of consideration are presented. It is demonstrated
how high order accuracy may be
achieved in the steady-state by respecting consistency in the formulation.
Report Titles
CSR 11-2001 Distributed Parallel Computation for Complex Rotational Flows of Non-Newtonian Fluids
A. Baloch and M.F. Webster
Complex rotational flows of non-Newtonian fluids are simulated through finite element
methods.The predictions have direct relevance to dough kneading, associated
with the food industry. The context is taken as two-dimensional and one of stirring
material within a cylindrical vessel. Three stirrer shapes are considered,placed in
eccentric location with respect to the cylinder centre.The motion is driven by the rotation
of the outer vessel wall. Variation with change in rheology and change in stirrer shapes
are analysed, with respect to flow kinematics, stress fields, rate-of-work
and power consumed.Computations are performed for Newtonian,shear-thinning
and viscoelastic fluids, at various viscosity levels to gradually approximate more realistic
dough-like response. For viscoelastic fluids,Phan-Thien/Tanner constitutive
models are adopted. The umerical method employed is based on a finite element
semi-implicit time-stepping Taylor-Galerkin/pressure-correction scheme, posed in
a cylindrical polar coordinate system. Simulations are conducted via distributed
parallel processing, performed on a networked cluster of workstations, employing
message passing. Parallel performance timings are compared against those obtained
working in sequential mode. Ideal linear speed-up with the number of processors is
observed for viscoelastic flows under this coarse-grained implementation.
Report Titles
CSR 12-2001 Numerical Study of Transient Instabilities in Reverse-Roller Coating Flows
M.S. Chandio and M.F. Webster
A semi-implicit Taylor-Galerkin/pressure-correction algorithm of a
transient finite element form is applied to analyse the flow instabilities that
commonly arise during reverse-roller coating. A mathematical model is derived to
describe the solvent coating applied to the underside of the sheet, assuming that the
lacquer is a Newtonian fluid and considering the flow between application roller
and foil. Here, we have investigated the effects of temporal instabilities, caused by
adjustment of nip-gap width and foil-position, extending our previous steady-state
analysis. Foil shifting is found to have a significant influence upon pressure and lift
on the foil, drag on the roller, and free coating profiles. This would result in
process instabilities, such as chatter and flow-lines. In contrast, nip-gap adjustment
has no influence on the coating finish.
Report Titles
CSR 13-2001 Simulation of Pressure- and Tube-tooling Wire-Coating Flows through DistributedComputation
A. Baloch, H. Matallah, V. Ngamaramvaranggul and M.F. Webster
This article focuses on the comparative study of annular wire-coating flows with polymer
melt materials. Different process designs are considered of pressure- and tube-tooling,
complementing earlier studies on individual designs. A novel mass-balance free-surface
location technique is proposed. The polymeric materials are represented via shearthinning,
differential viscoelastic constitutive models, taken of exponential Phan-
Thien/Tanner form. Simulations are conducted for these industrial problems through
distributed parallel computation, using a semi-implicit time-stepping Taylor-
Galerkin/pressure-correction algorithm. On typical field results and by comparing shortagainst
full-die pressure-tooling solutions, shear-rates are observed to increase ten fold,
while strain rates increase one hundred times. Tube-tooling shear and extension-rates are
one quarter of those for pressure-tooling. These findings across design options, have
considerable bearing on the appropriateness of choice for the respective process involved.
Parallel finite element results are generated on a homogeneous network of Intel-chip
workstations, running PVM (Parallel Vitual Machine) protocol over a Solaris operating
system. Parallel timings yield practically ideal linear speed-up over the set number of
processors.
Report Titles
CSR 14-2001 Image-Swept Volumes
Andrew S. Winter and Min Chen
Many graphical objects can be represented by swept volumes (including its subset
{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 elds as our underlying data type, and employ
volume ray casting techniques for rendering swept volumes in their original sweeping
speci cations 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 e ects. It also
facilitates the use of constructive volume geometry for creating complex scenes in
both modelling and rendering space.
Report Titles
CSR 15-2001 Development of an optimal hybrid finite volume/element method for viscoelastic flows
M. Aboubacar and M. F. Webster
A cell-vertex hybrid finite volume/element method is investigated that is implemented on triangles
and applied to the numerical solution of Oldroyd model fluids in contraction flows. Particular attention
is paid to establishing high-order accuracy, while retaining favourable stability properties in reaching
high levels of elasticity. The main impact of this study reveals that switching from quadratic to
linear finite volume stress representation with discontinuous stress gradients, and incorporating a local
reduced integration at the re-entrant corner, provide enhance stability properties. Solution smoothness
is achieved by adopting the non-conservative flux form with area integration, by appealing to quadratic
recovered velocity gradients, and through consistency considerations in the treatment of the time term
in the constitutive equation. In this manner, high-order accuracy is maintained, stability is ensured,
and the finer features of the flow are confirmed via mesh refinement. Lip vortices are observed for
We > 1, and a trailing-edge vortex is also apparent. Entry pressure drop, loss of evolution, and
solution asymptotic behaviour towards the re-entrant corner are also discussed.
Report Titles
CSR 16-2001 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