Domain decomposition using a 2-level correction scheme

The PHYSICA software was developed to enable multiphysics modelling allowing for interaction between Computational Fluid Dynamics (CFD) and Computational Solid Mechanics (CSM) and Computational Aeroacoustics (CAA). PHYSICA uses the finite volume method with 3-D unstructured meshes to enable the modelling of complex geometries. Many engineering applications involve significant computational time which needs to be reduced by means of a faster solution method or parallel and high performance algorithms. It is well known that multigrid methods serve as a fast iterative scheme for linear and nonlinear diffusion problems. This papers attempts to address two major issues of this iterative solver, including parallelisation of multigrid methods and their applications to time dependent multiscale problems.

The application of free-surface techniques to metal forming processes

In this paper the use of free-surface techniques, within the framework of a finite volume methodology, are investigated for the simulation of metal forming processes. In such processes, for example extrusion and forging, a workpiece is subjected to large scale deformation to create the product's shape. The use of Eulerian free-surface techniques to predict this final shape offers the advantage, over the traditionally used Lagrangian finite element method, of not requiring remmeshing. Two free-surface techniques to predict this final shape offers the advantage, over the traditionally used Lagrangian finite element method, of not requiring remesingh. Two free-surface techniques are compared by modelling a typical example of this type of process - non-Newtonian extrusion of an aluminium workpiece through a conical die.

[Review] M. Feistauer, J. Felcman, I. Straskbraba, Mathematical and Computational Methods for Compressible Flow, Oxford Science Publication, Oxford, ISBN 0198505884, 2004 (535pp.)

The growth of computer power allows the solution of complex problems related to compressible flow, which is an important class of problems in modern day CFD. Over the last 15 years or so, many review works on CFD have been published. This book concerns both mathematical and numerical methods for compressible flow. In particular, it provides a clear cut introduction as well as in depth treatment of modern numerical methods in CFD. This book is organised in two parts. The first part consists of Chapters 1 and 2, and is mainly devoted to theoretical discussions and results. Chapter 1 concerns fundamental physical concepts and theoretical results in gas dynamics. Chapter 2 describes the basic mathematical theory of compressible flow using the inviscid Euler equations and the viscous Navier–Stokes equations. Existence and uniqueness results are also included. The second part consists of modern numerical methods for the Euler and Navier–Stokes equations. Chapter 3 is devoted entirely to the finite volume method for the numerical solution of the Euler equations and covers fundamental concepts such as order of numerical schemes, stability and high-order schemes. The finite volume method is illustrated for 1-D as well as multidimensional Euler equations. Chapter 4 covers the theory of the finite element method and its application to compressible flow. A section is devoted to the combined finite volume–finite element method, and its background theory is also included. Throughout the book numerous examples have been included to demonstrate the numerical methods. The book provides a good insight into the numerical schemes, theoretical analysis, and validation of test problems. It is a very useful reference for applied mathematicians, numerical analysts, and practice engineers. It is also an important reference for postgraduate researchers in the field of scientific computing and CFD.

Modelling the Performance of Flexible Substrates for Lead-Free Applications

In this paper, the performance of flexible substrates for lead-free applications was studied using finite element method (FEM). Firstly, the thermal induced stress in the flex substrate during the lead free solder reflow process was predicted. The shear stress at the interface between the copper track and flex was plotted. This shear stress increases with the thickness of the copper track. Secondly, an ACF flip chip was taken as a typical lead-free application of the flex substrate. The reflow effect on the reliability of ACF interconnections was analyzed. Higher stress was identified along the interface between the conductive particle and the metallization, and the interfacial stress increases with the reflow peak temperature and the coefficient of thermal expansion (CTE) of the adhesive. The moisture effect on the reliability of ACF joints were studied using a macro-micro modeling technique, the predominantly tensile stress found at the interface between the conductive particle and metallization could reduce the contact area and even cause the electrical failure. Modeling results are consistent with the findings in the experimental work

Analyzing the performance of flexible substrates for lead-free applications

The performance of flexible substrates for lead-free applications was studied using finite element method (FEM). Firstly, the thermal induced stress in the flex substrate during the lead free solder reflow process was predicted. The shear stress at the interface between the copper track and flex was plotted. This shear stress increases with the thickness of the copper track and the thickness of the flex. Secondly, an anisotropic conductive film (ACF) flip chip was taken as a typical lead-free application of the flex substrate and the moisture effect on the reliability of ACF joints were studied using a 3D macro-micro modeling technique. It is found that the time to be saturated of an ACF flip chip is much dependent on the moisture diffusion rate in the polyimide substrate. The majority moisture diffuses into the ACF layer from the substrate side rather than the periphery of the ACF. The moisture induced stress was predicted and the predominant tensile stress was found at the interface between the conductive particle and metallization which could reduce the contact area and even cause the electrical failure

Semi-Lagrange time integration for PDE models of asian options

Semi-Lagrange time integration is used with the finite difference method to provide accurate stable prices for Asian options, with or without early exercise. These are combined with coordinate transformations for computational efficiency and compared with published results

Numerical simulation of flow-induced cavity noise in self-sustained oscillations

The generation and near-field radiation of aerodynamic sound from a low-speed unsteady flow over a two-dimensional automobile door cavity is simulated by using a source-extraction-based coupling method. In the coupling procedure, the unsteady cavity flow field is first computed solving the Reynolds averaged Navier–Stokes (RANS) equations. The radiated sound is then calculated by using a set of acoustic perturbation equations with acoustic source terms which are extracted from the time-dependent solutions of the unsteady flow. The aerodynamic and its resulting acoustic field are computed for the Reynolds number of 53,266 based on the base length of the cavity. The free stream flow velocity is taken to be 50.9m/s. As first stage of the numerical investigation of flow-induced cavity noise, laminar flow is assumed. The CFD solver is based on a cell-centered finite volume method. A dispersion-relation-preserving (DRP), optimized, fourth-order finite difference scheme with fully staggered-grid implementation is used in the acoustic solver

Microwave modelling and validation in food thawing applications

Developing temperature fields in frozen cheese sauce undergoing microwave heating were simulated and measured. Two scenarios were investigated: a centric and offset placement on the rotating turntable. Numerical modeling was performed using a dedicated electromagnetic Finite Difference Time Domain (FDTD) module that was two-way coupled to the PHYSICA multiphysics package. Two meshes were used: the food material and container were meshed for the heat transfer and the microwave oven cavity and waveguide were meshed for the microwave field. Power densities obtained on the structured FDTD mesh were mapped onto the unstructured finite volume method mesh for each time-step/turntable position. On heating for each specified time-step the temperature field was mapped back onto the FDTD mesh and the electromagnetic properties were updated accordingly. Changes in thermal/electric properties associated with the phase transition were fully accounted for as well as heat losses from product to cavity. Detailed comparisons were carried out for the centric and offset placements, comparing experimental temperature profiles during microwave thawing with those obtained by numerical simulation.

Reliability analysis for power electronics modules

This paper discusses the reliability of power electronics modules. The approach taken combines numerical modeling techniques with experimentation and accelerated testing to identify failure modes and mechanisms for the power module structure and most importantly the root cause of a potential failure. The paper details results for two types of failure (i) wire bond fatigue and (ii) substrate delamination. Finite element method modeling techniques have been used to predict the stress distribution within the module structures. A response surface optimisation approach has been employed to enable the optimal design and parameter sensitivity to be determined. The response surface is used by a Monte Carlo method to determine the effects of uncertainty in the design.

Multiphysics simulation of microwave curing in micro-electronics packaging applications

Purpose – This paper aims to present an open-ended microwave curing system for microelectronics components and a numerical analysis framework for virtual testing and prototyping of the system, enabling design of physical prototypes to be optimized, expediting the development process. Design/methodology/approach – An open-ended microwave oven system able to enhance the cure process for thermosetting polymer materials utilised in microelectronics applications is presented. The system is designed to be mounted on a precision placement machine enabling curing of individual components on a circuit board. The design of the system allows the heating pattern and heating rate to be carefully controlled optimising cure rate and cure quality. A multi-physics analysis approach has been adopted to form a numerical model capable of capturing the complex coupling that exists between physical processes. Electromagnetic analysis has been performed using a Yee finite-difference time-domain scheme, while an unstructured finite volume method has been utilized to perform thermophysical analysis. The two solvers are coupled using a sampling-based cross-mapping algorithm. Findings – The numerical results obtained demonstrate that the numerical model is able to obtain solutions for distribution of temperature, rate of cure, degree of cure and thermally induced stresses within an idealised polymer load heated by the proposed microwave system. Research limitations/implications – The work is limited by the absence of experimentally derived material property data and comparative experimental results. However, the model demonstrates that the proposed microwave system would seem to be a feasible method of expediting the cure rate of polymer materials. Originality/value – The findings of this paper will help to provide an understanding of the behaviour of thermosetting polymer materials during microwave cure processing.

Predicting the reliability of power electronic modules

This paper discusses the reliability of an IGBT power electronics module. This work is part of a major UK funded initiative into the design, packaging and reliability of power electronic modules. The predictive methodology combines numerical modeling techniques with experimentation and accelerated testing to identify failure modes and mechanisms for these type of power electronic module structures. The paper details results for solder joint failure substrate solder. Finite element method modeling techniques have been used to predict the stress and strain distribution within the module structures. Together with accelerated life testing, these results have provided a failure model for these joints which has been used to predict reliability of a rail traction application

Open ended microwave oven for packaging

A novel open waveguide cavity resonator is presented for the combined variable frequency microwave curing of bumps, underfills and encapsulants, as well as the alignment of devices for fast flip-chip assembly, direct chip attach (DCA) or wafer-scale level packaging (WSLP). This technology achieves radio frequency (RF) curing of adhesives used in microelectronics, optoelectronics and medical devices with potential simultaneous micron-scale alignment accuracy and bonding of devices. In principle, the open oven cavity can be fitted directly onto a flip-chip or wafer scale bonder and, as such, will allow for the bonding of devices through localised heating thus reducing the risk to thermally sensitive devices. Variable frequency microwave (VFM) heating and curing of an idealised polymer load is numerically simulated using a multi-physics approach. Electro-magnetic fields within a novel open ended microwave oven developed for use in micro-electronics manufacturing applications are solved using a dedicated Yee scheme finite-difference time-domain (FDTD) solver. Temperature distribution, degree of cure and thermal stresses are analysed using an Unstructured Finite Volume method (UFVM) multi-physics package. The polymer load was meshed for thermophysical analysis, whilst the microwave cavity - encompassing the polymer load - was meshed for microwave irradiation. The two solution domains are linked using a cross mapping routine. The principle of heating using the evanescent fringing fields within the open-end of the cavity is demonstrated. A closed loop feedback routine is established allowing the temperature within a lossy sample to be controlled. A distribution of the temperature within the lossy sample is obtained by using a thermal imaging camera.

The Development of a Two-Dimensional Transient Catalyst Model for Direct Injection Two-Stroke Applications.

This paper describes the development of a two-dimensional transient catalyst model. Although designed primarily for two-stroke direct injection engines, the model is also applicable to four-stroke lean burn and diesel applications. The first section describes the geometries, properties and chemical processes simulated by the model and discusses the limitations and assumptions applied. A review of the modeling techniques adopted by other researchers is also included. The mathematical relationships which are used to represent the system are then described, together with the finite volume method used in the computer program. The need for a two-dimensional approach is explained and the methods used to model effects such as flow and temperature distribution are presented. The problems associated with developing surface reaction rates are discussed in detail and compared with published research. Validation and calibration of the model is achieved by comparing predictions with measurements from a flow reactor. While an extensive validation process, involving detailed measurements of gas composition and thermal gradients, has been completed, the analysis is too detailed for publication here and is the subject of a separate technical paper.

Micromachined 300GHz high Q resonant slot frequency selective surface filter

The design of a low loss quasi-optical beam splitter which is required to provide efficient diplexing of the bands 316.5-325.5 GHz and 349.5-358.5 GHz is presented. To minimise the filter insertion loss, the chosen architecture is a three-layer freestanding array of dipole slot elements. Floquet modal analysis and finite element method computer models are used to establish the geometry of the periodic structure and to predict its spectral response. Two different micromachining approaches have been employed to fabricate close packed arrays of 460 mm long elements in the screens that form the basic building block of the 30mm diameter multilayer frequency selective surface. Comparisons between simulated and measured transmission coefficients for the individual dichroic surfaces are used to determine the accuracy of the computer models and to confirm the suitability of the fabrication methods.

Investigation of precision grinding process for production of silicon diaphragms

The application of precision grinding for the formation of a silicon diaphragm is investigated. The test structures involved 2-6 mm diam diaphragms with thicknesses in the range of 25-150 //m. When grinding is performed without supporting the diaphragm, bending occurs due to nonuniform removal of the silicon material over the diaphragm region. The magnitude of bending depends on the µNal thickness of the diaphragm. The results demonstrate that the use of a porous silicon support can significantly reduce the amount of bending, by a factor of up to 300 in the case of 50 m thick diaphragms. The use of silicon on insulator (SOI) technology can also suppress or eliminate bending although this may be a less economical process. Stress measurements in the diaphragms were performed using x-ray and Raman spectroscopies. The results show stress of the order of 1 X107-! X108 Pa in unsupported and supported by porous silicon diaphragms while SOI technology provides stress-free diaphragms. Results obtained from finite element method analysis to determine deterioration in the performance of a 6 mm diaphragm due to bending are presented. These results show a 10% reduction in performance for a 75 µm thick diaphragm with bending amplitude of 30 fim, but negligible reduction if the bending is reduced to