CSR 1-2000 The Algebraic Structure of Interface Definition Languages and Architectures
D.Ll.L. Rees, K. Stephenson and J.V. Tucker
In this paper we examine formally a notion of architecture
for the design of systems. The basic idea is that:
CSR 2-2000 Coordinate Free Programming of Computational Fluid Dynamics Problems
P.W. Grant, M. Haveraaen and M.F. Webster
It has long been acknowledged that the development of scientific
applications is in
need of better software engineering practices. Here we contrast the
difference between conventional software development of CFD codes
with a method based on coordinate free mathematics.
The former approach leads to programs where different
aspects, such as the discretisation technique and the coordinate systems, can
get entangled with the solver algorithm.
The latter approach yields programs that segregate these concerns into fully
independent software modules.
Such considerations are important for the construction of numerical
codes for practical problems. The two approaches are illustrated on
the coating problem:
the simulation of coating a wire with a polymer.
Report Titles
CSR 3-2000 Correctness and Verification of Hardware Systems Using Maude
N.A. Harman
We consider models of hardware systems, within a well-developed set of
mathematical tools based on an equational, algebraic model. We implement
these tools using Maude, an equational, algebraic language with strong
meta-language tools and an efficient term rewriting implementation. Maude
has the
same mathematical basis as the existing formal tools and it is fast. We
consider the process of verification, and apply it to a simple illustrative
pipeline.
Microprocessors, and related systems, are modelled as iterated maps.
Initialisation functions act as an invariant when applying one-step theorems
to reduce formal verification to state exploration.
Report Titles
CSR 4-2000 Verifying a Simple Pipelined Microprocessor Using Maude
N.A.Harman
We consider the verification of a simple pipelined microprocessor in Maude,
by implementing an equational theoretical model of systems. Maude is an
equationally-based language, with an efficient term rewriting
implementation, and effective meta-level tools. Microprocessors and other
systems are modelled as iterated maps operating in time over some
state-set, and are related by means of data and abstraction maps, and
correctness is reduced to state exploration by the choice of an appropriate
initialisation function, ensuring/enforcing consistency of the initial
state.
Report Titles
CSR 5-2000 JACIE - an Authoring Language for Rapid Prototyping Net-centric, Multimedia and Collaborative Applications
Abdul S. Haji-Ismail, Min Chen, Phil W. Grant and Mark Kiddell
With continuous acceptance of World Wide Web (WWW) as a de facto
standard for human-computer interaction and human-human communication, it
is desirable to develop net-centric, multimedia and collaborative applications.
In this paper, we present a new scripting language called JACIE, which is designed
to support rapid prototyping and implementation of such applications. In particular,
we highlight the necessity to support the management of multimedia interaction
and communication in collaborative applications, and describe how JACIE facilitates
such support through the concepts of channels and a collection of built-in 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 multimedia software engineering tool.
Report Titles
CSR 6-2000 Embedded Recovery Methods for Viscoelastic Flow Past a Sphere in a Cylindrical Tube
H. Matallah, P. Townsend and M.F. Webster
The motivation for this study is to capture the superior
accuracy properties of recovery methods and
their application to the numerical solution of nonlinear
viscoelastic flows. For velocity gradient recovery,
local direct methods are compared to Galerkin least
squares methods. Superconvergence properties are intrinsic.
We compare and contrast averaging and patch
recovery approaches. We investigate the properties
of such schemes and their influence upon stability by
focusing on flow past a sphere in a cylindrical tube.
Report Titles
CSR 7-2000 Embedded Recovery Methods for Viscoelastic Flow
H. Matallah, P. Townsend and M.F. Webster
We analyse different 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, a start-up
channel
flow and a flow past a sphere. Such benchmark flows 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
Domain representations of partial functions, with applications to spatial objects and constructive volume geometry
J. Blanck, V. Stoltenberg-Hansen and J. V. Tucker
A partial spatial object is a partial map from space to data. Data
types of partial spatial objects are modelled by topological algebras
of partial maps and are the foundation for a high level approach to
volume graphics called constructive volume geometry (CVG), where space
and data are subspaces of n-dimensional Euclidean space. We
investigate the computability of partial spatial object data types, in
general and in volume graphics, using the theory of effective domain
representations for topological algebras. The basic mathematical
problem considered is to classify which partial functions between
topological spaces can be represented by total continuous functions
between given domain representations of the spaces. We prove theorems
about partial functions on regular Hausdorff spaces and their domain
representations, and apply the results to partial spatial objects and
CVG algebras.
Report Titles
Streams, stream transformers and domain representations
J. Blanck, V. Stoltenberg-Hansen and J. V. Tucker
We present a general theory for the computation of stream transformers
of the form F: (R -> B) -> (T -> A) , where time T and R , and
data A and B , are discrete or continuous. We show how methods for
representing topological algebras by algebraic domains can be applied
to transformations of continuous streams. A stream transformer is
continuous in the compact-open topology on continuous streams if, and
only if, it has a continuous lifting to a standard algebraic domain
representation of such streams. We also examine the important problem
of representing discontinuous streams, such as signals T -> A , where
time T is continuous and data A is discrete.
Report Titles
Two and Three Dimensional Distributed Computations for Viscoelastic Cavity Flows
A. Baloch, P.W. Grant and M.F. Webster
A finite element study of incompressible viscoelastic ows in a planar
lid-driven cavity is presented. The
hardware platform is a network combination of both
homogeneous and heterogeneous clusters of workstations.
A semi-implicit time-stepping Taylor-Galerkin
scheme is employed with Parallel Virtual Machine
(PVM) message passing libraries as the message passing protocol.
Both DEC-alpha and Intel Solaris clusters
are utilised. Parallel results are compared against single processor
(sequentially) solutions, using the parallelism paradigm of domain
decomposition. Linear
speed-up with the number of processors is realised.
Report Titles
Three-Dimensional Numerical Simulation of Dough Kneading
D.Ding and M.F. Webster
In this article we report on work concerned with
the three-dimensional numerical simulation of dough
mixing that arises in the food processing industry.
Two dough mixers at various rotation speeds are
studied, one with one stirrer and the other with two
stirrers. Various types of fluid models are
incorporated in this work. Numerical simulations are
based on three dimensions in the cylindrical
coordinates system. The results reflect excellent
agreements against 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
On Consistency of Cell-Vertex Finite-Volume Formulations for Viscoelastic Flow
M.S. Chandio and M.F. Webster
The accuracy, stability and consistency of a new
cell-vertex hybrid finite element/volume scheme is investigated
in the numerical solution of a model viscoelastic sink flow.
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 beachieved in the steady-state
by respecting consistency in the formulation.
Report Titles
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 wire-
coating 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.
Report Titles
CSR 14-2000 The Algebraic Structure of Interface Definition Languages and Architectures (Revised Version)
D.Ll.L. Rees, K. Stephenson and J.V. Tucker In this paper (a revision of CSR1-2000) we examine formally a notion of architecture for the design of systems, based on the idea that the architecture of a system can be modelled by the structure of its interface expressed in terms of the interfaces for its components. Thus,
System Architecture = Structured set of (sub)-system interfaces.
We specify a general model for interface definition languages (IDLs) based on this idea and the idea that an:Interface = Name + Imports + Body.
A set of interfaces is a repository. An interface architecture is a repository with some primary interfaces identified; the import dependencies between the interfaces of a repository are used to determine its structure.The general model is made using algebraic specifications to define the abstract syntax of a general IDL. The model provides a framework for making an algebraic specification of a specific IDL in a modular way and allows interface transformations to be defined by structural induction.
We use the general model to derive a simple IDL suitable for the design phase of object-oriented software development. This requires us to specify a form of Body that treats both data types and state, and in Body we explicitly distinguish between methods with and without side-effects, by commands and queries, respectively. We also consider other proposals for Body that yield new IDLs, including other object-oriented design languages and data type specification languages.
On the accuracy and stability properties of an 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 equa-
tion. 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
Homogeneous and Heterogeneous Distributed Cluster Processing for Two and Three-Dimensional Viscoelastic Flows
A. Baloch, P.W. Grant and M.F. Webster
A finite element study of two and three-dimensional
incompressible viscoelastic flows in a planar lid-driven cavity and
concentric rotating cylinders is presented. The hardware platforms
consist of both homogeneous and heterogeneous clusters of
workstations. A semi-implicit time-stepping Taylor-Galerkin scheme is
employed using the message passing mechanism provided by the Parallel
Virtual Machine (PVM) libraries. DEC-alpha, Intel Solaris and
AMD-K7(Athlon) Linux clusters are utilised. Parallel results are
compared against single processor (sequentially) solutions, using the
parallelism paradigm of domain decomposition. Communication is
effectively masked and practically ideal, linear speed-up with the
number of processors is realised.
Report Titles
Highly elastic solutions of Oldroyd-B and Phan-Thien Tanner fluids with a hybrid finite volume/element method: planar contraction flows
M. Aboubacar, H. Matallah and M.F. Webster
Finite element and finite volume methods are analysed through the computation of
inertialess flows of viscoelastic fluids in plane 4:1 sharp and rounded corner contraction
geometries. Simulations are presented for three models: a constant viscosity Oldroyd-
B fluid, and PTT shear thinning fluids of exponential and linear approximation. A
Taylor-Galerkin/Pressure-correction scheme is implemented as the base time-stepping
framework. The momentum equations are solved by a finite element method, whilst the
constitutive equations are solved by a finite volume approach and compared to
a finite
element scheme. Mesh convergence is analysed via three different meshes,
refined around
the re-entrant corner to capture the boundary layer structure. Specialist techniques are
implemented for the finite volume scheme and the sharp corner problem, lowering the
order of approximation of the solution in the neighbourhood of the singularity. For the
Oldroyd-B model, higher values of Weissenberg numbers are reached with these
finite
volume schemes compared to their finite element counterparts.
Report Titles