Shape-optimized mesh partitioning and load balancing for parallel adaptive FEM

We present a dynamic distributed load balancing algorithm for parallel, adaptive Finite Element simulations in which we use preconditioned Conjugate Gradient solvers based on domain-decomposition. The load balancing is designed to maintain good partition aspect ratio and we show that cut size is not always the appropriate measure in load balancing. Furthermore, we attempt to answer the question why the aspect ratio of partitions plays an important role for certain solvers. We define and rate different kinds of aspect ratio and present a new center-based partitioning method of calculating the initial distribution which implicitly optimizes this measure. During the adaptive simulation, the load balancer calculates a balancing flow using different versions of the diffusion algorithm and a variant of breadth first search. Elements to be migrated are chosen according to a cost function aiming at the optimization of subdomain shapes. Experimental results for Bramble's preconditioner and comparisons to state-of-the-art load balancers show the benefits of the construction.

Magnetic levitation fluid dynamics

This work is concerned with the accurate computation of flow in a rapidly deforming liquid metal droplet, suspended in an AC magnetic field. Intense flow motion due to the induced electromagnetic force distorts dynamically the droplet envelope, which is initially spherical. The relative positional change between the liquid metal surface and the surrounding coil means that fluid flow and magnetic field computations need to be closely coupled. A spectral technique is used to solve this problem, which is assumed axisymmetric. The computed results are compared against a physical experiment and "ideal sphere" analytic solutions. A comparison between the "magnetic pressure" approximation and the full electromagnetic force solutions, shows fundamental differences; the full electromagnetic force solution is necessary for accurate results in most practical applications of this technique. The physical reason for the fundamental discrepancy is the difference in the electromagnetic force representation: only the gradient part of the full force is accounted for in the "magnetic pressure" approximation. Figs 9, Refs 13.

Finite volume methods applied to the computational modelling of welding phenomena

This paper presents the computational modelling of welding phenomena within a versatile numerical framework. The framework embraces models from both the fields of computational fluid dynamics (CFD) and computational solid mechanics (CSM). With regard to the CFD modelling of the weld pool fluid dynamics, heat transfer and phase change, cell-centred finite volume (FV) methods are employed. Additionally, novel vertex-based FV methods are employed with regard to the elasto-plastic deformation associated with the CSM. The FV methods are included within an integrated modelling framework, PHYSICA, which can be readily applied to unstructured meshes. The modelling techniques are validated against a variety of reference solutions.

Parallel performance in multi-physics simulation

A comprehensive simulation of solidification/melting processes requires the simultaneous representation of free surface fluid flow, heat transfer, phase change, non-linear solid mechanics and, possibly, electromagnetics together with their interactions in what is now referred to as "multi-physics" simulation. A 3D computational procedure and software tool, PHYSICA, embedding the above multi-physics models using finite volume methods on unstructured meshes (FV-UM) has been developed. Multi-physics simulations are extremely compute intensive and a strategy to parallelise such codes has, therefore, been developed. This strategy has been applied to PHYSICA and evaluated on a range of challenging multi-physics problems drawn from actual industrial cases.

Multiphase mesh partitioning for parallel computational mechanics codes

We consider the load-balancing problems which arise from parallel scientific codes containing multiple computational phases, or loops over subsets of the data, which are separated by global synchronisation points. We motivate, derive and describe the implementation of an approach which we refer to as the multiphase mesh partitioning strategy to address such issues. The technique is tested on example meshes containing multiple computational phases and it is demonstrated that our method can achieve high quality partitions where a standard mesh partitioning approach fails.

A coarse grid extraction of sound signals for computational aeroacoustics

Sound waves are propagating pressure fluctuations, which are typically several orders of magnitude smaller than the pressure variations in the flow field that account for flow acceleration. On the other hand, these fluctuations travel at the speed of sound in the medium, not as a transported fluid quantity. Due to the above two properties, the Reynolds averaged Navier–Stokes equations do not resolve the acoustic fluctuations. This paper discusses a defect correction method for this type of multi-scale problems in aeroacoustics. Numerical examples in one dimensional and two dimensional are used to illustrate the concept. Copyright (C) 2002 John Wiley & Sons, Ltd.

Performance evaluation of a distributed algorithm for an inverse heat conduction problem

Numerical solutions of realistic 2-D and 3-D inverse problems may require a very large amount of computation. A two-level concept on parallelism is often used to solve such problems. The primary level uses the problem partitioning concept which is a decomposition based on the mathematical/physical problem. The secondary level utilizes the widely used data partitioning concept. A theoretical performance model is built based on the two-level parallelism. The observed performance results obtained from a network of general purpose Sun Sparc stations are compared with the theoretical values. Restrictions of the theoretical model are also discussed.

Two fluid approach to high speed impact interaction amongst solid structures

The issues surrounding collision of projectiles with structures has gained a high profile since the events of 11th September 2001. In such collision problems, the projectile penetrates the stucture so that tracking the interface between one material and another becomes very complex, especially if the projectile is essentially a vessel containing a fluid, e.g. fuel load. The subsequent combustion, heat transfer and melting and re-solidification process in the structure render this a very challenging computational modelling problem. The conventional approaches to the analysis of collision processes involves a Lagrangian-Lagrangian contact driven methodology. This approach suffers from a number of disadvantages in its implementation, most of which are associated with the challenges of the contact analysis component of the calculations. This paper describes a 'two fluid' approach to high speed impact between solid structures, where the objective is to overcome the problems of penetration and re-meshing. The work has been carried out using the finite volume, unstructured mesh multi-physics code PHYSICA+, where the three dimensional fluid flow, free surface, heat transfer, combustion, melting and re-solidification algorithms are approximated using cell-centred finite volume, unstructured mesh techniques on a collocated mesh. The basic procedure is illustrated for two cases of Newtonian and non-Newtonian flow to test various of its component capabilities in the analysis of problems of industrial interest.

Representing the dividing instant

The so-called dividing instant (DI) problem is an ancient historical puzzle encountered when attempting to represent what happens at the boundary instant which divides two successive states. The specification of such a problem requires a thorough exploration of the primitives of the temporal ontology and the corresponding time structure, as well as the conditions that the resulting temporal models must satisfy. The problem is closely related to the question of how to characterize the relationship between time periods with positive duration and time instants with no duration. It involves the characterization of the ‘closed’ and ‘open’ nature of time intervals, i.e. whether time intervals include their ending points or not. In the domain of artificial intelligence, the DI problem may be treated as an issue of how to represent different assumptions (or hypotheses) about the DI in a consistent way. In this paper, we shall examine various temporal models including those based solely on points, those based solely on intervals and those based on both points and intervals, and point out the corresponding DI problem with regard to each of these temporal models. We shall propose a classification of assumptions about the DI and provide a solution to the corresponding problem.

Modelling electromagnetically levitated liquid droplet oscillations

This work comprises accurate computational analysis of levitated liquid droplet oscillations in AC and DC magnetic fields. The AC magnetic field interacting with the induced electric current within the liquid metal droplet generates intense fluid flow and the coupled free surface oscillations. The pseudo-spectral technique is used to solve the turbulent fluid flow equations for the continuously dynamically transformed axisymmetric fluid volume. The volume electromagnetic force distribution is updated with the shape and position change. We start with the ideal fluid test case for undamped Rayleigh frequency oscillations in the absence of gravity, and then add the viscous and the DC magnetic field damping. The oscillation frequency spectra are further analysed for droplets levitated against gravity in AC and DC magnetic fields at various combinations. In the extreme case electrically poorly conducting, diamagnetic droplet (water) levitation dynamics are simulated. Applications are aimed at pure electromagnetic material processing techniques and the material properties measurements in uncontaminated conditions.

AC & DC magnetic levitation and semi-levitation modelling

This work presents computation analysis of levitated liquid thermal and flow fields with free surface oscillations in AC and DC magnetic fields. The volume electromagnetic force distribution is continuously updated with the shape and position change. The oscillation frequency spectra are analysed for droplets levitation against gravity in AC and DC magnetic fields at various combinations. For larger volume liquid metal confinement and melting the semi-levitation induction skull melting process is simulated with the same numerical model. Applications are aimed at pure electromagnetic material processing techniques and the material properties measurements in uncontaminated conditions.

Modelling induction skull melting design modifications

Induction Skull Melting (ISM) is a technique for heating, melting, mixing and, possibly, evaporating reactive liquid metals at high temperatures with a minimum contact at solid walls. The presented numerical modelling involves the complete time dependent process analysis based on the coupled electromagnetic, temperature and turbulent velocity fields during the melting and liquid shape changes. The simulation model is validated against measurements of liquid metal height, temperature and heat losses in a commercial size ISM furnace. The observed typical limiting temperature plateau for increasing input electrical power is explained by the turbulent convective heat losses. Various methods to increase the superheat within the liquid melt, the process energy efficiency and stability are proposed.

Obtaining data to validate a model of an induction skull melting furnace

A casting route is often the most cost-effective means of producing engineering components. However, certain materials, particularly those based on Ti, TiAl and Zr alloy systems, are very reactive in the molten condition and must be melted in special furnaces. Induction Skull Melting (ISM) is the most widely-used process for melting these alloys prior to casting components such as turbine blades, engine valves, turbocharger rotors and medical prostheses. A major research project is underway with the specific target of developing robust techniques for casting TiAl components. The aims include increasing the superheat in the molten metal to allow thin section components to be cast, improving the quality of the cast components and increasing the energy efficiency of the process. As part of this, the University of Greenwich (UK) is developing a computer model of the ISM process in close collaboration with the University of Birmingham (UK) where extensive melting trials are being undertaken. This paper describes the experimental measurements to obtain data to feed into and to validate the model. These include measurements of the true RMS current applied to the induction coil, the heat transfer from the molten metal to the crucible cooling water, and the shape of the column of semi-levitated molten metal. Data are presented for Al, Ni and TiAl.

The effect of reflow process on the contact resistance and reliability of anisotropic conductive film interconnection for flip chip on flex applications

The work presented in this paper focuses on the effect of reflow process on the contact resistance and reliability of anisotropic conductive film (ACF) interconnection. The contact resistance of ACF interconnection increases after reflow process due to the decrease in contact area of the conducting particles between the mating I/O pads. However, the relationship between the contact resistance and bonding parameters of the ACF interconnection with reflow treatment follows the similar trend to that of the as-bonded (i.e. without reflow) ACF interconnection. The contact resistance increases as the peak temperature of reflow profile increases. Nearly 40% of the joints were found to be open after reflow with 260 °C peak temperature. During the reflow process, the entrapped (between the chip and substrate) adhesive matrix tries to expand much more than the tiny conductive particles because of the higher coefficient of thermal expansion, the induced thermal stress will try to lift the bump from the pad and decrease the contact area of the conductive path and eventually, leading to a complete loss of electrical contact. In addition, the environmental effect on contact resistance such as high temperature/humidity aging test was also investigated. Compared with the ACF interconnections with Ni/Au bump, higher thermal stress in the Z-direction is accumulated in the ACF interconnections with Au bump during the reflow process owing to the higher bump height, thus greater loss of contact area between the particles and I/O pads leads to an increase of contact resistance and poorer reliability after reflow.