Viscoelastic flow through a planar contraction using a semi-Lagrangian finite volume method

A semi-Lagrangian finite volume scheme for solving viscoelastic flow problems is presented. A staggered grid arrangement is used in which the dependent variables are located at different mesh points in the computational domain. The convection terms in the momentum and constitutive equations are treated using a semi-Lagrangian approach in which particles on a regular grid are traced backwards over a single time-step. The method is applied to the 4 : 1 planar contraction problem for an Oldroyd B fluid for both creeping and inertial flow conditions. The development of vortex behaviour with increasing values of We is analyzed.

A semi-Lagrangian finite volume method for Newtonian contraction flows

A new finite volume method for solving the incompressible Navier--Stokes equations is presented. The main features of this method are the location of the velocity components and pressure on different staggered grids and a semi-Lagrangian method for the treatment of convection. An interpolation procedure based on area-weighting is used for the convection part of the computation. The method is applied to flow through a constricted channel, and results are obtained for Reynolds numbers, based on half the flow rate, up to 1000. The behavior of the vortex in the salient corner is investigated qualitatively and quantitatively, and excellent agreement is found with the numerical results of Dennis and Smith [Proc. Roy. Soc. London A, 372 (1980), pp. 393-414] and the asymptotic theory of Smith [J. Fluid Mech., 90 (1979), pp. 725-754].

Does an incremental filling technique reduce polymerization shrinkage stresses

It is widely accepted that volumetric contraction and solidification during the polymerization process of restorative composites in combination with bonding to the hard tissue result in stress transfer and inward deformation of the cavity walls of the restored tooth. Deformation of the walls decreases the size of the cavity during the filling process. This fact has a profound influence on the assumption-raised and discussed in this paper-that an incremental filling technique reduces the stress effect of composite shrinkage on the tooth. Developing stress fields for different incremental filling techniques are simulated in a numerical analysis. The analysis shows that, in a restoration with a well-established bond to the tooth-as is generally desired-incremental filling techniques increase the deformation of the restored tooth. The increase is caused by the incremental deformation of the preparation, which effectively decreases the total amount of composite needed to fill the cavity. This leads to a higher-stressed tooth-composite structure. The study also shows that the assessment of intercuspal distance measurements as well as simplifications based on generalization of the shrinkage stress state cannot be sufficient to characterize the effect of polymerization shrinkage in a tooth-restoration complex. Incremental filling methods may need to be retained for reasons such as densification, adaptation, thoroughness of cure, and bond formation. However, it is very difficult to prove that incrementalization needs to be retained because of the abatement of shrinkage effects.

Multilevel mesh partitioning for optimizing domain shape

Multilevel algorithms are a successful class of optimization techniques that address the mesh partitioning problem for mapping meshes onto parallel computers. They usually combine a graph contraction algorithm together with a local optimization method that refines the partition at each graph level. To date, these algorithms have been used almost exclusively to minimize the cut-edge weight in the graph with the aim of minimizing the parallel communication overhead. However, it has been shown that for certain classes of problems, the convergence of the underlying solution algorithm is strongly influenced by the shape or aspect ratio of the subdomains. Therefore, in this paper, the authors modify the multilevel algorithms to optimize a cost function based on the aspect ratio. Several variants of the algorithms are tested and shown to provide excellent results.

Multilevel mesh partitioning for optimising aspect ratio

Multilevel algorithms are a successful class of optimisation techniques which address the mesh partitioning problem. They usually combine a graph contraction algorithm together with a local optimisation method which refines the partition at each graph level. To date these algorithms have been used almost exclusively to minimise the cut-edge weight, however it has been shown that for certain classes of solution algorithm, the convergence of the solver is strongly influenced by the subdomain aspect ratio. In this paper therefore, we modify the multilevel algorithms in order to optimise a cost function based on aspect ratio. Several variants of the algorithms are tested and shown to provide excellent results.

Mesh partitioning: a multilevel balancing and refinement algorithm

Multilevel algorithms are a successful class of optimization techniques which addresses the mesh partitioning problem. They usually combine a graph contraction algorithm together with a local optimization method which refines the partition at each graph level. In this paper we present an enhancement of the technique which uses imbalance to achieve higher quality partitions. We also present a formulation of the Kernighan-Lin partition optimization algorithm which incorporates load-balancing. The resulting algorithm is tested against a different but related state-of-the-art partitioner and shown to provide improved results.

Multilevel mesh partitioning for heterogeneous communication networks

Multilevel algorithms are a successful class of optimisation techniques which address the mesh partitioning problem for distributing unstructured meshes onto parallel computers. They usually combine a graph contraction algorithm together with a local optimisation method which refines the partition at each graph level. To date these algorithms have been used almost exclusively to minimise the cut edge weight in the graph with the aim of minimising the parallel communication overhead, but recently there has been a perceived need to take into account the communications network of the parallel machine. For example the increasing use of SMP clusters (systems of multiprocessor compute nodes with very fast intra-node communications but relatively slow inter-node networks) suggest the use of hierarchical network models. Indeed this requirement is exacerbated in the early experiments with meta-computers (multiple supercomputers combined together, in extreme cases over inter-continental networks). In this paper therefore, we modify a multilevel algorithm in order to minimise a cost function based on a model of the communications network. Several network models and variants of the algorithm are tested and we establish that it is possible to successfully guide the optimisation to reflect the chosen architecture.

A cell-centred finite volume method for modelling viscoelastic flow

An unstructured cell-centred finite volume method for modelling viscoelastic flow is presented. The method is applied to the flow through a planar channel and the 4:1 planar contraction for creeping flow of an Oldroyd-B fluid. The results are presented for a range of Weissenberg numbers. In the case of the planar channel results are compared with analytical solutions. For the 4:1 planar contraction benchmark problem the convection terms in the constitutive equations are approximated using both first and second order differencing schemes to compare the techniques and the effect of mesh refinement on the solution is investigated. This is the first time that a fully unstructured, cell-centredfinitevolume technique has been used to model the Oldroyd-B fluid for the test cases presented in this paper.

Using EMGs and kinematics data to study the take-off technique of experts and novices for a pole vaulting short run-up educational exercise

This study attempts to characterise the electromyographic activity and kinematics exhibited during the performance of take-off for a pole vaulting short run-up educational exercise, for different expertise levels. Two groups (experts and novices) participated in this study. Both groups were asked to execute their take-off technique for that specific exercise. Among the kinematics variables studied, the knee, hip and ankle angles and the hip and knee angular velocities were significantly different. There were also significant differences in the EMG variables, especially in terms of (i) biceps femoris and gastrocnemius lateralis activity at touchdown and (ii) vastus lateralis and gastrocnemius lateralis activity during take-off. During touchdown, the experts tended to increase the stiffness of the take-off leg to decrease braking. Novices exhibited less stiffness in the take-off leg due to their tendency to maintain a tighter knee angle. Novices also transferred less energy forward during take-off due to lack of contraction in the vastus lateralis, which is known to contribute to forward energy transfers. This study highlights the differences in both groups in terms of muscular and angular control according to the studied variables. Such studies of pole vaulting could be useful to help novices to learn expert's technique.

The impact of powder flowing properties on dosator filling system operation

Purpose: To study the impact of powder flow properties on dosator filling systems, with particular focus on improvements in dose weight accuracy and repeatability. Method: This study evaluates a range of critical powder flow properties such as: flow function, cohesion, wall friction, adhesion to wall surfaces, density/compressibility data, stress ratio “K” and gas permeability. The characterisations of the powders considered in this study were undertaken using an annular shear cell using a sample size of 0.5 litres. This tester also incorporated the facility to measure bed expansion during shear in addition to contraction under consolidation forces. A modified Jenike type linear wall friction tester was used to develop the failure loci for the powder sample in conjunction with multiple wall samples (representing a variety of material types and surface finishes). Measurements of the ratio of applied normal stress versus lateral stress were determined using a piece of test equipment specifically designed for the purpose. Results: The correct characterisation of powders and the incorporation of this data into the design of process equipment are recognised as critical for reliable and accurate operation. An example of one aspect of this work is the stress ratio “K”. This characteristic is not well understood or correctly interpreted in many cases – despite its importance. Fig 1 [Omitted] (illustrates a sample of test data. The slope of the line gives the stress ratio in a uniaxial compaction system – indicating the behaviour of the material under compaction during dosing processes. Conclusions: A correct assessment of the bulk powder properties for a given formulation can allow prediction of: cavity filling behaviour (and hence dosage), efficiency of release from dosator, and strength and stability of extruded dose en route to capsule filling Influences over the effectiveness of dosator systems have been shown to be impacted upon by: bed pre-compaction history, gas permeability in the bed (with respect to local density effects), and friction effects for materials of construction for dosators