Browsing by Author "Forth, S. A."
Now showing 1 - 4 of 4
Results Per Page
Sort Options
Item Open Access Indirect boundary element methods for modelling bubbles under three dimensional deformation(2009-01-22T16:40:48Z) Lindkvist, Gaute; Forth, S. A.The nonlinear behaviour of gas and vapour bubbles is a complex phenomenon which plays a signi cant role in many natural and man-made processes. For example, bubbles excited by an acoustic eld play important roles in lithotripsy, drug delivery, ultrasonic imaging, surface cleaning and give rise to the phenomenon of sonoluminescence (light emission from a bubble excited by sound). In such contexts, the oscillation of even a single bubble is not yet fully understood, let alone the behaviour of multiple bubbles interacting with each other. An essential part of understanding such problems is un- derstanding the complex and sometimes unpredictable coupling between the oscillation of the bubble volume and the bubble shape, a problem requiring experimental research, theoretical work and numerical studies. In this Thesis we focus on numerical simulation of a single gas bubble oscillating in a free liquid. Previously, such numerical simulations have al- most exclusively assumed axisymmetry and small amplitude oscillations. To avoid these assumptions we build upon and extend previous boundary ele- ment methods used for three dimensional simulations of other bubble prob- lems. We use high order elements and parallel processing to yield an indirect boundary element method capable of capturing ne surface e ects on three dimensional bubbles subjected to surface tension, over extended periods of time. We validate the method against the classical Rayleigh-Plesset equation for spherical oscillation problems before validating the indirect boundary el- ement method and the method used by Shaw (2006), against each other, on several small amplitude axisymmetric oscillation problems. We then proceed to study near-resonant non-axisymmetric shape oscillations of order 2 and 4 and the e ect these oscillations have on higher order modes, with a level of detail we believe has not been achieved in a non-axisymmetric study before. We also con rm some predictions made by Pozrikidis' on resonant interac- tions between the second order modes and the volume mode in addition. Finally we study the spherical instability of a bubble trapped in a uniform acoustic eld, demonstrating, as expected, that instabilities show up in all resonant shape modes, including non-axisymmetric ones.Item Open Access Mathematical and numerical modelling of shock initiation in heterogeneous solid explosives(Cranfield University, 2008-07-17T10:27:51Z) Whitworth, N.; Forth, S. A.In the field of explosive science, the existence of the ‘hot-spot’ is generally accepted as essential to any theory on shock initiation. Continuum-based shock initiation models only account for ‘hot-spots’ implicitly, and the majority of these models use pressure-dependent reaction rates. The development of a simple but physically realistic model to predict desensitisation (double shock) effects within the confines of an existing pressure-based model is described and simulations compared with experimental data with mixed results. The need to invoke a separate desensitisation model for double shocks demonstrates that reaction rates are not substantially dependent on local pressure. The newly developed continuum, entropy-dependent, CREST model has been implemented and validated in a number of hydrocodes. However, the move to entropy-based reaction rates introduces a number of computational problems not associated with pressure-based models. These problems are described, in particular, an entropy-dependent model over-predicts the rate of energy release in an explosive adjacent an impact surface, and requires a finer mesh than a pressure-dependent model to achieve mesh converged results. The CREST model, fitted only to onedimensional data of the shock to detonation transition, is shown to be able to accurately simulate two-dimensional detonation propagation data. This gives confidence in the predictive capability of the model. To account for ‘hot-spots’ explicitly, a simple model to describe ‘hot-spot’ initiation has been developed. The simple model is presented where ‘hot-spots’ are formed as a result of elastic-viscoplastic stresses generated in the solid explosive during pore collapse. Results from the model compare well with corresponding results from direct numerical simulations, and both are consistent with observations and commonly held ideas regarding the shock initiation and sensitivity of heterogeneous solid explosives. The results also indicate that viscoplastic ‘hot-spot’ models described in the literature are built on an invalid assumption.Item Open Access MATLAB automatic differentiation using source transformation(2012-06-28) Kharche, R. V.; Forth, S. A.This thesis presents our work on compiler techniques to implement Algo- rithmic Di erentiation (AD) using source transformation in MATLAB. AD is concerned with the accurate and e cient computation of derivatives of complicated mathematical functions represented by computer programs. Source transformation techniques for AD, whilst complicated to imple- ment, are known to yield derivative code with better run-time e ciency than methods using overloading support of the underlying language. We present results from MSAD that con rm the increase in e ciency using source trans- formed code for MATLAB AD. Most importantly, we demonstrate the use of a unique compiler code specialisation method to implement AD. We also assert the need for compiler optimisations in MATLAB, especially in the con- text of AD, and showcase MSAD as an extensible infrastructure to implement new optimisations and algorithms for AD or other applications. Where other e orts on MATLAB AD are implemented using operator overloading or a mix of overloading and source transformation, MSAD (Springer LNCS, Vol. 3994, 2006) was the rst to generate di erentiated MATLAB code using source transformation alone. MSAD is also the only e ort to implement source transformed AD by resolving overloaded MAT- LAB code. The existing MAD package (ACM TOMS, 32, No.2, 2006) pro- vides a highly e cient overloaded implementation of MATLAB AD. MSAD uses compiler code specialisation techniques to specialise and inline fmad and derivvec overloaded operations of the MAD package in order to generate MATLAB AD code. The operator overloading overheads inherent in MAD are eliminated while preserving the derivvec class's optimised derivative combination operations. As a compiler framework for MATLAB, MSAD demonstrates a novel use of an existing e ective compiler algorithm (Sparse Conditional Constant Propagation) to infer properties of MATLAB variables such as type, rank, shape, sparsity and value by propagating a composite lattice of all the prop- erties together.Item Open Access Uncertainty estimation using the moments method facilitated by automatic differentiation in Matlab(2010-03-26T09:39:52Z) Menshikova, M.; Forth, S. A.Computational models have long been used to predict the performance of some baseline design given its design parameters. Given inconsistencies in manufacturing, the manufactured product always deviates from the baseline design. There is currently much interest in both evaluating the effects of variability in design parameters on a design’s performance (uncertainty estimation), and robust optimization of the baseline design such that near optimal performance is obtained despite variability in design parameters. Traditionally, uncertainty analysis is performed by expensive Monte-Carlo methods. This work considers the alternative moments method for uncertainty propagation and its implementation in Matlab. In computational design it is assumed a computational model gives a sufficiently accurate approximation to a design’s performance. As such it can be used for estimating statistical moments (expectation, variance, etc.) of the design due to known statistical variation of the model’s parameters, e.g., by the Monte Carlo approach. In the moments method we further assume the model is sufficiently differentiable that a Taylor series approximation to a model may be constructed, and the moments of the Taylor series may be taken analytically to yield approximations to the model’s moments. In this thesis we generalise techniques considered within the engineering community and design and document associated software to generate arbitrary order Taylor series approximations to arbitrary order statistical moments of computational models implemented in Matlab; Taylor series coefficients are calculated using automatic differentiation. This approach is found to be more efficient than a standard Monte Carlo method for the small-scale model test problems we consider. Previously Christianson and Cox (2005) have indicated that the moments method will be non-convergent in the presence of complex poles of the computational model and suggested a partitioning method to overcome this problem. We implement a version of the partitioning method and demonstrate that it does result in convergence of the moments method. Additionally, we consider, what we term, the branch detection problem in order to ascertain if our Taylor series approximation might only be valid piecewise.