Rozprawy doktorskie na temat „Numerical modelling”

Until recently, research has been scarce in the field of physical modelling of dam breaching. Over the past few years, teams from the University of Ottawa, Canada, Delft University of Technology, Netherlands, and HR Wallingford, United Kingdom have worked on several physical models to help determine how various dam breaching characteristics vary due to changes in dam geometry and geotechnical properties. The purpose of this project is to use these new experimental data sets to compare and validate the applicability range of two existing pieces of software, MIKE11-DB and BREACH developed by the Danish Hydraulic Institute and National Weather Service, respectively. Several breaching characteristics such as the outflow hydrograph, peak flow, lag time, breaching time, breach width, and water level are considered in the present study. A sensitivity analysis is also performed on the model’s main input parameters and their sensitivity and performance is ranked accordingly.

This thesis reports onreview and research work carried out on the numerical analysis of elastomers. The two numerical techniques investigated for this purpose are the finite and boundary element methods. The finite element method is studied so that existing theory is used to develop a finite element code both to review the finite element method as applied to the stress analysis of elastomers and to provide a comparison of results and numerical approach with the boundary element method. The research work supported on in this thesis covers the application of the boundary element method to the stress analysis of elastomers. To this end a simplified regularization approach is discussed for the removal of strong and hypersingularities generated in the system on non-linear boundary integral equations. The necessary programming details for the implementation of the boundary element method are discussed based on the code developed for this research. Both the finite and boundary element codes developed for this research use the Mooney-Rivlin material model as the strain energy based constitutive stress strain function. For validation purposes four test cases are investigated. These are the uni-axial patch test, pressurized thick wall cylinder, centrifugal loading of a rotating disk and the J-Integral evaluation for a centrally cracked plate. For the patch test and pressurized cylinder, both plane stress and strain have been investigated. For the centrifugal loading and centrally cracked plate test cases only plane stress has been investigated. For each test case the equivalent results for an equivalent FEM program mesh have been presented. The test results included in this thesis prove that the FE and BE derivations detailed in this work are correct. Specifically the simplified domain integral singular and hyper-singular regularization approach was shown to lead to accurate results for the test cases detailed. Various algorithm findings specific to the BEM implementation of the theory are also discussed.

In the processing industries particulate materials are often in the form of powders which themselves are agglomerations of much smaller sized particles. During powder processing operations agglomerate degradation occurs primarily as a result of collisions between agglomerates and between agglomerates and the process equipment. Due to the small size of the agglomerates and the very short duration of the collisions it is currently not possible to obtain sufficiently detailed quantitative information from real experiments to provide a sound theoretically based strategy for designing particles to prevent or guarantee breakage. However, with the aid of computer simulated experiments, the micro-examination of these short duration dynamic events is made possible. This thesis presents the results of computer simulated experiments on a 2D monodisperse agglomerate in which the algorithms used to model the particle-particle interactions have been derived from contact mechanics theories and, necessarily, incorporate contact adhesion. A detailed description of the theoretical background is included in the thesis. The results of the agglomerate impact simulations show three types of behaviour depending on whether the initial impact velocity is high, moderate or low. It is demonstrated that high velocity impacts produce extensive plastic deformation which leads to subsequent shattering of the agglomerate. At moderate impact velocities semi-brittle fracture is observed and there is a threshold velocity below which the agglomerate bounces off the wall with little or no visible damage. The micromechanical processes controlling these different types of behaviour are discussed and illustrated by computer graphics. Further work is reported to demonstrate the effect of impact velocity and bond strength on the damage produced. Empirical relationships between impact velocity, bond strength and damage are presented and their relevance to attrition and comminution is discussed. The particle size distribution curves resulting from the agglomerate impacts are also provided. Computer simulated diametrical compression tests on the same agglomerate have also been carried out. Simulations were performed for different platen velocities and different bond strengths. The results show that high platen velocities produce extensive plastic deformation and crushing. Low platen velocities produce semi-brittle failure in which cracks propagate from the platens inwards towards the centre of the agglomerate. The results are compared with the results of the agglomerate impact tests in terms of work input, applied velocity and damage produced.

In this project, a numerical model describing the reaction mechanism and the mass and energy transport in wood pyrolysis is studied. The applicability of the model in predicting actual biomass pyrolysis assessed by comparing the model to TGA experimental measurements. The comparison to experiments is done in relation to the mass loss characteristics of chips of varying sizes. The mass loss is of interest as it is a variable necessary in the coupling of reactor and particle models. Three reaction models were simulated and results compared to experimental data, namely, the reaction model developed by Park et al. [Combustion and Flame 157 (2010) 481-494], a simple multicomponent parallel reaction model, and a competitive reaction model. The model of Park et al. did not fit with the experimental data as it underestimates the char yield. The parallel reaction model, which is based on hemicellulose and cellulose decomposition to char and volatiles, also did not agree with the experiments even when fitting the parameters to the data. The downward trend of char yield with increasing temperature suggests there exists competition between the volatiles and char in wood pyrolysis. The proposed competitive reaction model which consists of a hemicellulose reaction to volatiles and a cellulose reaction to volatiles and char is in good agreement with the experimental data. The mass loss characteristics in the experimental temperature range is fairly predicted within reasonable accuracy.

Předkládaná práce je zaměřena na numerické modelování spalování tuhých paliv na roštu metodami výpočtové dynamiky tekutin (CFD). Jelikož výsledky CFD simulací roštového spalování závisí na kvalitě vstupních dat, která zahrnují i údaje o teplotě, hmotnostním toku a chemickém složení spalin vystupujících z lože, pozornost je věnována především procesům, probíhajícím v loži během spalování na roštu. Velká část práce je věnována vývoji spolehlivého modelu spalování v sypaných ložích, jelikož může napomoci zkvalitnit výsledky simulací i rozšířit znalosti principů spalování tuhých paliv v sypaných ložích. V rámci práce byl vyvinut jednorozměrný nestacionární model spalování v experimentálním reaktoru a implementován do počítačového programu GRATECAL 1.3 včetně grafického uživatelského rozhraní. Zvláštní důraz byl kladen na konzervativnost modelu. Proto byla vyvinuta metoda pro kontrolu hmotnostní a energetické bilance systému a následně aplikována v řadě studií, v rámci nichž byly odhaleny některé chyby týkající se definic zdrojových členů, které byly převzaty z literatury a opraveny. Pomocí modelu byla provedena analýza šíření čela sušení a reakce hoření koksu po výšce lože pšeničné slámy. Na základě výsledků těchto analýz bylo doporučeno zahrnout i modelování změny porozity částic paliva, aby šířka reakční zóny byla predikována korektně v případě, že je uvažována změna porozity celého lože. Rovněž vyvinutá bilanční metoda byla použita k analýze vlivu kritérií konvergence na hmotnostní a energetickou nerovnováhu simulovaného systému. Bylo zjištěno, že škálovaná rezidua rovnic všech veličin by měla poklesnout aspoň na hodnotu $10^{-6}$, aby bylo dosaženo nízké hmotnostní a energetické nerovnováhy a tudíž uspokojivě přesných výsledků ze simulací v loži. Druhá část práce je věnována vývoji a implementaci knihovny uživatelem definovaných funkcí pro komerční CFD nástroj ANSYS FLUENT, které slouží k propojení modelu lože s modelem komory reálné spalovací jednotky, aby byla umožněna dynamická změna okrajových podmínek na vstupu do komory v závislosti na výstupech ze simulací v loži. Vytvořené rozhraní pro propojení těchto dvou modelů je dostatečně obecné pro aplikaci na širokou škálu modelů roštových kotlů. Popsané výsledky přispívají k lepšímu porozumění numerickému modelování spalování na roštu, a to zejména ve fázi sestavování numerického modelu a nastavení parametrů řešiče pro kontrolu konvergence.

Flameless combustion can be adopted as a low-emission combustion regime in the aviation sector, which is one of the biggest contributors to NOx emissions and is expected to grow in the near future. Nevertheless, several issues must be solved before any practical applications. Effective design procedure must deal with either combustion or heat transfer phenomena occurring at extremely low—temperature conditions. To this aim, experimental and numerical analyses focused on the characterization of fuel/oxidant behaviour are strongly needed and represent an essential step for further development. Besides, the complexity of the analysed technological system requires advanced tools for the definition of the chemical kinetics, for the burner designs and more in general for the definition of aviation equipment design. In this light, the thesis has been addressed to the study of flameless combustion mechanisms within a combustion chamber prototype developed in the Faculty of Aerospace Engineering at TU Delft. In particular, the temperature and species concentration fields have been analysed. The CFD tool which will be used is Ansys Fluent together with two detailed reaction mechanisms (KIBO and RDM19).

La tesis se centra en el desarrollo de técnicas numéricas específicas para la resolución de problemas de mecánica de sólidos, tomando como referencia aquellos que involucran geomateriales (suelos, rocas, materiales granulares,...). Concretamente, se tratan los siguientes puntos: 1) formulaciones Arbitrariamente Lagrangianas Eulerianas (ALE) para problemas con grandes desplazamientos del contorno; 2) métodos de resolución para problemas no lineales en el campo de la mecánica de sólidos y 3) modelización del comportamiento mecánico de materiales granulares mediante leyes constitutivas elastoplásticas.
Las principales aportaciones de la tesis son: el desarrollo de una formulación ALE para modelos hyperelastoplásticos y el cálculo de operadores tangentes para distintas leyes constitutivas y esquemas de integración temporal no triviales (uso de esquemas de derivación numérica, técnicas de subincrementación y modelos elastoplásticos con endurecimiento y/o reblandecimiento dependientes del trabajo plástico o la densidad). Se presentan diversas aplicaciones que muestran las principales características de los desarrollos presentados (análisis del ensayo del molinete para arcillas blandas, del ensayo triaxial para arenas, de la rotura bajo una cimentación, del proceso de estricción de una barra metálica circular y de un proceso de estampación en frío), dedicando una especial atención a los aspectos computacionales de la resolución de dichos problemas. Por último, se dedica un capítulo específico a la modelización y la simulación numérica de procesos de compactación fría de polvos metálicos y cerámicos.
Numerical modelling of problems involving geomaterials (i.e. soils, rocks, concrete and ceramics) has been an area of active research over the past few decades. This fact is probably due to three main causes: the increasing interest of predicting the material behaviour in practical engineering situations, the great change of computer capabilities and resources, and the growing interaction between computational mechanics, applied mathematics and different engineering fields (concrete, soil mechanics...). This thesis fits within this last multidisciplinary approach. Based on constitutive modelling and applied mathematics and using both languages the numerical simulation of some complex geomechanical problems has been studied.

The state of the art regarding experiments, constitutive modelling, and numerical simulations involving geomaterials is very extensive. The thesis focuses in three of the most important and actual ongoing research topics within this framework: 1) the treatment of large boundary displacements by means of Arbitrary Lagrangian-Eulerian (ALE) formulations; 2) the numerical solution of highly nonlinear systems of equations in solid mechanics; and 3) the constitutive modelling of the nonlinear mechanical behaviour of granular materials. The three topics have been analysed and different contributions for each one of them have been developed. Moreover, some of the new developments have been applied to the numerical modelling of cold compaction processes of powders. The process consists in transforming a loose powder into a compacted sample through a large volume reduction. This problem has been chosen as a reference application of the thesis because it involves large boundary displacements, finite deformations and highly nonlinear material behaviour. Therefore, it is a challenging geomechanical problem from a numerical modelling point of view.

The most relevant contributions of the thesis are the following: 1) with respect to the treatment of large boundary displacements: quasistatic and dynamic analyses of the vane test for soft materials using a fluid-based ALE formulation and different non-newtonian constitutive laws, and the development of a solid-based ALE formulation for finite strain hyperelastic-plastic models, with applications to isochoric and non-isochoric cases; 2) referent to the solution of nonlinear systems of equations in solid mechanics: the use of simple and robust numerical differentiation schemes for the computation of tangent operators, including examples with several non-trivial elastoplastic constitutive laws, and the development of consistent tangent operators for different substepping time-integration rules, with the application to an adaptive time-integration scheme; and 3) in the field of constitutive modelling of granular materials: the efficient numerical modelling of different problems involving elastoplastic models, including work hardening-softening models for small strain problems and density-dependent hyperelastic-plastic models in a large strain context, and robust and accurate simulations of several powder compaction processes, with detailed analysis of spatial density distributions and verification of the mass conservation principle.

The principle purpose of this research is to resolve the mode of failure of the Heather Hill landslide, one of several well defined failures in the Beaver Valley, Glacier National Park, British Columbia. Field work led to the preliminary conclusion that some type of toppling process contributed to the failure. A literature review of toppling revealed that large scale topples have never been quantitatively assessed, and that currently used analytical techniques are not adequate. Consideration of alternative numerical techniques resulted in the distinct element method being selected as the best technique for modelling toppling. The Universal Distinct Element Code (UDEC) was purchased and its suitability demonstrated by reevaluating examples of toppling analysis reported in the literature, and evaluating a large scale engineered slope at Brenda mine where toppling is known to occur. UDEC is used to examine and classify the mode of failure of the Heather Hill slide. This research leads to very important general conclusions on toppling and specific conclusions relating to the Heather Hill landslide: UDEC is suitable for modelling all types of topples. The program can be used to back analyze rock mass strength parameters and determine the shape and location of the final failure surface in flexural toppling. A quantitative assessment with UDEC confirms that the base of failure in flexural toppling may be planar or curvilinear, and that pore pressures significantly affect stability. The Heather Hill landslide failed by flexural toppling limiting to a curvilinear failure surface, and the slope immediately north of the Heather Hill landslide is deformed by flexural toppling. The locations of landslides in the Beaver Valley correspond with the occurrence of foliated pelitic rocks in the lower slopes and the boundary between these rocks and stronger grits is the up slope limit. The kinematic test of toppling potential is violated by the Heather Hill landslide. This test is shown to only apply to small scale drained slopes.
Science, Faculty of
Earth, Ocean and Atmospheric Sciences, Department of
Graduate

District heating is today, in Sweden, the most common method used for heating buildings in cities. More than half of all the buildings, both commercial and residential, are heated using district heating. The load on the district heating networks are affected by, among other things, the time of the day and different external conditions, such as temperature differences. One has to be able to simulate the heat and pressure losses in the network in order to deliver the amount of heat demanded by the customers. Expansions of district heating networks and disrupted pipes also demand good simulations of the networks. To cope with this, energy companies use simulation software. These software need to contain numerical methods that provide accurate and stable results and at the same time be fast and efficient. At the moment there are available software packages that works but these have some limitations. Among other things you may need to divide the whole network into smaller loops or try to guess how the distribution of pressure and flow in the network looks like. The development in recent years makes it possible to use better and more efficient algorithms for these types of problems. The purpose of this report is therefore to introduce a better and more efficient method than that used in the current situation. This work is the first step in order to replace a current method used in a simulation software provided by Vitec energy. Therefore, we will in this report, stick to computing pressure and flow in the network. The method we will introduce in this report is called the gradient method and it is based on the Newton Raphson method. Unlike with older methods like Hardy Cross which is a relaxation method, you do not have to divide the network into loops. Instead you create a matrix representation of the network that is used in the computations. The idea is also that you should not need to make good initial guesses to get the method to converge quickly. We performed a number of test simulations in order to examine how the method performs. We tested how different initial guesses and how different sizes of the networks affected the number of iterations. The results shows that the model is capable of solving large networks within a reasonable number of iterations. The results also show that the initial guesses have little impact on the number of iterations. Changing the initial guess on the pressure does not affect the number at all but it turns out that changing the initial guess on the flow can affect the number of iterations a little, but not much.

Headphone design is facilitated by modelling and has traditionally been carried out using lumped parameters, which are efficient but limited to low frequencies. In this investigation a wave based approach is taken using finite elements to introduce a headphone modelling tool which has the capability to predict high frequency harmonic components in the acoustic field. The development of these increased bandwidth headphone modelling capabilities is carried out over 3 discrete design phases involving 2D axisymmetric and 3D models with the key components being the porous cushion, the headphone driver and the geometric profile of the pinna. The cushion is represented using a well established 6 parameter porous material model as an equivalent fluid which is a convenient approach for a finite element implementation. Characterisation of porous materials using such an approach generally involves an expensive and time consuming measurement regime; this investigation has shown that multi-dimensional optimisation gives an adequate representation without need for this. Simulations using the finite element model headphone model are compared against measurements taken on a HATS mannequin and show good agreement up to 10 kHz, a significant improvement in bandwidth over previous publications. An investigative survey was carried out using these software tools of various headphone dimensional parameters, including a representation of pinna variation which, significantly, shows wide variations in frequency responses at high frequency. If used as an indication of inter-subject variation it suggests the ability to model accurately to a high frequency may only have limited benefits for headphones intended for many different wearers.

The understanding of the masticatory apparatus including its functional and structural relationship with other components of the cranium increasingly requires an interdisciplinary approach. Recently, "traditional biological sciences" such as anatomy, comparative biology, anthropology and evolution have increasingly meshed with elements from other domains, such as mechanical engineering and material sciences, which has resulted in new and exciting paradigms to be explored. This is particularly true in the field of craniofacial biomechanics yet there are still many unexplored issues and numerous questions that remain unanswered. Numerical modelling in general and Finite Element Analysis (FEA) in particular, represent a numerical experimental procedure to generate such information. Originally derived from the field of structural engineering, FEA has steadily permeated its way into craniofacial biomechanics and has proven itself as a most useful scientific tool. The present study introduces an engineering-based workframe for applying FEA to craniofacial biomechanical research in a comprehensive manner to cover the entire analytical spectrum, from developing questions to providing their solutions. The study is composed of two major experimental parts addressing both the linear elastic and the non-linear behaviour of some biomaterials encountered in the craniofacial arena. In the first part I analysed mandibular biomechanics using linear elastic models while in the second part I used nonlinear discrete models to determine the optimal elastic properties of the cervical restorative materials. Modern humans have a number of anatomical features that set us apart from our ancestors. Amongst these perhaps the most striking is the emergence of a protruding chin, otherwise absent in other archaic humans and hominids. While it has been shown that the chin has its embryological origins in the postnatal remodelling of bone in the area around the mandibular symphysis which produces the midline keel in the form of an inverted �T� the functional significance of this novel evolutionary feature is still obscure. It is accepted that the mandible is optimally designed for resisting masticatory stress, whereby optimal is seen as maximual strength at the lowest biological cost. Here, I tested the currently most accepted theory, namely that the chin provides mechanical resistance to the mandible during mastication. In other words, I tested the hypothesis that a chinned mandible would be stiffer and hence experience lower strains when compared to a non-chinned counterpart under identical loadings. My functional analysis consisted firstly of three simple models which reproduce a simian shelf, a flat and a chinned symphysis, loaded using two unidirectional loadcases (torsion and wishboning) to represent a distortion similar to that which occurs in the mandible during mastication. Secondly, I developed complex geometrical models which incorporated the cortical bone, medullary bone and teeth. The models were then analysed using the same loadcases as those used for the first theoretical models. Additionally, I incorporated the coronal bending and also a coupled loadcase which simulated the complex deformation of the mandible during biting. The aim here was to test the hypothesis that the presence of a chin changed the strain pattern in the mastication-loaded mandible. The results were then interpreted using Frost�s mechanostat theory which relates in a more precise manner the mechanical loading environment to the adaptive response of the bone. My results showed that the calculated strain values for both the chinned and flat mandibles were within the normal bone maintenance levels of the mechanostat during molar biting. In other words, variation in bone strain magnitude across the mandible, which should differ between the chinned and the non-chinned mandibles if the hypothetical mechanical role of the chin is true, is similar in both forms. I concluded that the development of the human chin is thus unrelated to the functional demands placed upon it by mastication. I suggested a new functional demand associated with pronounced tongue activity during speech. I hypothesise that it is the resistance to stresses induced by strong, repetitive contractions of the tongue and perioral musculature during, phonation that shaped the modern human chin. I tested my hypothesis by loading the symphyseal region with two principal nonmasticatory, muscle systems; firstly, the tongue and secondly the peri-oral muscular curtain, anterior to the symphysis. My results suggested that the flat, non-chinned symphysis when subjected to speech-related genioglossal movements will undergo adaptive changes which would result in an optimised (chinned) shape, such as that found in the modern human symphysis. These results thus offer a new foundation to an old hypothesis and a solution to the longstanding controversy over the origin of the human chin. I conclude that forces generated by speech rather than those generated by mastication, shaped the chin in anatomically modern humans. Prompted by an earlier observation I further investigated the apparent cross-over distribution of strains on the mandibular corpora during mastication. In doing so, I tested the hypothesis that this cross-over may be linked with another particular anatomical feature of the mandible that of the postcanine cortical asymmetry, which appears to be stereotypical among anthropoids. The results of my study hence suggest that strain patterns within the human mandible are more complex than previously thought. Not only do strains differ between lingual and buccal aspects of working and non-working sides, but they also differ within these areas (i.e. from alveolus to corpus, to lower border regions). I conclude that postcanine cortical asymmetry may be a retained evolutionary trait rather than the result of masticatory biomechanics. In the second section of the thesis I introduced a different analysis regime which allows the prediction of fracture initiation and propagation. In this part I analysed the mechanics underlying the failure of the restorations placed in non-carious cervical lesions and suggested changes in the material properties of the restorations used to treat them. Non-carious cervical lesions (NCCL) include those entities characterised by the cervical loss of hard dental tissue that occurs in the absence of any carious process. To distinguish between lesions that occur due to excessive occlusal load and other non-carious cervical lesion (i.e. erosion and abrasion) the clinical term "abfraction" has been adopted. Although a common clinical issue, failure of restoration placed in these lesions has not been subjected to a rigorous biomechanical analysis. To determine which of the material�s parameters should be changed and to what extent, I employed a combined numerical approach. Here I introduced a novel approach in simulating the cracking of restorative materials and tooth tissues which is based on a simpler material formulation and can be used in an advanced nonlinear numerical analysis. The material model I used allows automatic crack insertion and growth and also uniquely accounts for the microdamage which precedes the instalment of macroscopic cracks. The first step was to balance the factors that may affect failure employing a linear analysis with a stress-based approach to failure. Here, the aim was to investigate the influence of lesion shape and depth as well as the direction of occlusal loading on the mechanical response of the cervical glass-ionomer cements restoration in a lower first premolar. This analysis showed that the direction of loading was the major contributor to the failure of the restoration. The next step was to apply this fracture model to the restorations of the NCCL in order to verify if the material is able to accurately simulate the location and type of mechanical failure. The data for this problem, i.e. the geometry and the loadcase were derived from the conclusions of linear analysis, that is I chose the "worst case scenario" as the upper boundary of material endurance. My results showed that under the action of para-functional loadings the GIC failed on the cervical margin. I also showed that prior to fracture the restorative material undergoes strain softening, which in turn introduces damage and weakens the materials involved. After successfully testing the proposed model, the final step was to determine which material properties and restorative techniques would be most reliable under given biomechanical conditions. The present work relied on the hypothesis that a more flexible material would partially buffer the local stress concentration and hence reduce the likelihood of mechanical failure of the restoration. My study, a first of its kind, proposes a radical approach to address the problems of material improvement, namely: numerical-based material optimisation engineering. That is, I aimed to identify the "most favourable" selection of elastic modulus or E value for the restorative material, which will allow it to survive under the unfavourable occlusal loading conditions that may prevail. Two filling techniques were considered; firstly a single bulk material, namely glass-ionomer (GIC) and secondly a layered technique. The latter consisted of a layer of GIC supporting a composite bulk restorative. I chose two thicknesses for the GIC layer, 50 and 150 microns. My results showed that the restorative materials currently used in cervical non-carious lesions are largely unsuitable in terms of resistance to fracture of the restoration mostly because of their relative high stiffness irrespective of the filling technique. The best results are obtained for a bulk filling with a 1GPa elastic modulus material case in which the tensile stresses are about 50% of the failure limit. This approach in determining the mechanical properties of the restorative is novel and unique so far in the dental literature. The direct benefit of this study was the improvement of the restorative material, as it can be engineered to withstand the conditions identified as major cause of failure. This is consonant with the call for new materials better tailored for some specific needs.

The spillway of Sarpfossen hydropower plant has been studied numerically and experimentally. The physical model was built in the Vassdragslaboratoriet at the Norwegian University of Science and Technology, NTNU. The model consists of the Sarpfossen dam and the river Glomma upstream of the dam. On the spillway crest are three gates installed - two flap gates and a sector gate. In addtion is further upstream of the dam a bridge for cars and trains. Two of the bridge piers are fixed in the water and has an influence in the flow pattern. The model was run with a certain discharge and the velocities in the river were measured with a Flow Meter and VectrinoVelocimeter. Besides of the velocity measurements the water levels between bridge and dam were measured. These measurements were conducted to investigate the occuring wave phenomena, shock wave. The simulations were carried out by a commercial program, STAR-CCM+. The results from the simulation have been verified by the measurements from the model. Simulation were performed to replicate the flow phenomenas in the physical model and to find out how well STAR-CCM+ is suited to cope the complex flow structures. Three simulations were performed - two for the velocity distribution and one for the water level measurements with generated shock waves. The results of the simulations show quite good correlations. The velocity measurements show satisfying results. The shock wave could also be replicated quite well and the results are quite promising. Future studies are recommended to get more experience with simulating complex free-surface flows. Especially simulations of shock wave are not very frequent and well tested and should be included in further studies.

This research project focuses on the application of numerical modelling methods to rock mechanics problems, combining theoretical, experimental and numerical modelling work. Specifically, practical finite difference modelling approach for analysing shaft lining stability through the Marl and Potash strata at Boulby mine UK has been developed using the commercially available software FLAC2D/FLAC3D (ITASCA 2008). A soft rock Marl occurs close to the bottom of the two deep shafts at the mine. Both shafts concrete linings through this stratum have suffered considerable pressure, which has caused gradual failure of the shaft lining. So far, both shaft linings through the Marl stratum have been restored twice after sunk in 1970s and a further third relining is now required and being planned. The in situ observations, the rock engineers's experience, and the available in situ measurements at the mine have been significantly helpful in the validation of the numerical modelling. Many factors at the mine site have, however, made this numerical modelling research challenging, including complicated lining structures, complex lining failure conditions and the scarcity of laboratory test data for the weakest rock material - the Marl, which easily weathers on exposure. Based on a comprehensive literature review, a database of materials properties relevant to this research has been produced. The methodology of obtaining appropriate rock mass input material properties to use in numerical modelling based on laboratory test data has been studied. In three-dimensional models in this research, two modelling methods have been developed to simulate each stage in the shaft linings: the continuous model for all shaft linings and independent models for each shaft lining. The numerical modelling results imply that: Firstly, in the independent three-dimensional models, the modelling results were difficult to understand due to the complexity of the structures representing the shaft relining systems and difficulty in defining appropriate properties for the interface elements. Therefore, the continuous three-dimensional model that gives the analysable modelling results is recommended by the author for this research. By this method, the effect of the historic changes in the stress field on each shaft lining's stability can be investigated from initial shaft construction to subsequent relining phases. Secondly, the weak rock Marl should not be the only reason for the shaft linings' failure through this stratum. The roadway approximately 10 m beneath the Marl stratum was also a key factor for the stability of the shaft linings. The weak Marl cannot carry the stress redistribution around the shaft caused by the roadway excavation, which was an uneven loading acting on the circular shaft linings. This uneven loading introduced high shear and tensile stresses which threatened the stability of the circular concrete structures. Thirdly, the interface materials between high strength concrete blocks in shaft relinings improved the flexibility of the lining systems successfully, but decreased the strength of the whole lining systems as weak "joints". In addition, the single ring concrete blocks (the first and third relinings) are a more effective lining than the double rings (the second relining), and the third relining would perform better than the previous ones. As a recommendation for the further simulation, it is worth attempting to simulate the longer term deformation and stress conditions of the shaft concrete lining systems using the Creep model built in FLAC2D/FLAC3D codes. Additionally, deeper research work combined with in situ investigation can be done to decrease the uncertainty of the input material properties to make the numerical models as close to the real engineering situation as possible.

The intention of this thesis is to gain a better understanding of basic physical processes occurring in low temperature plasmas. This is achieved by applying both analytic and numerical models. Low temperature plasmas are found in both technological and astrophysical contexts. Three different situations are investigated: an instability in electronegative plasmas; electron avalanches during plasma initiation; and a phenomenon called the Critical Ionisation Velocity interaction. Industrial plasma discharges with electronegative gases are found to be unstable in certain conditions. Fluctuations in light emission, particle number densities and potential are observed. The instability has been reproduced in a variety of experiments. Reports from the experiments are discussed to characterise the key features of the instability. An, as yet un-considered, physical process that could explain the instability is introduced. The instability relies on the plasma's transparency to the electric field. This mechanism is investigated using simple zero-dimensional numerical and analytic models. The results from the models are compared to experimental results. The calculated frequencies are in good agreement with the experimental measurements. This shows that the instability mechanism described here is relevant. For the remaining two problems a three-dimensional particle model is constructed. This model calculates the trajectories of each individual particle. The potential field is solved self-consistently on a computational mesh. Poisson's equation is solved using a Multigrid technique. This iterative solution method uses many grids, of different resolutions, to smooth the error on all spatial scales. The mathematical foundation and details of the components of the Multigrid method are presented. Several test cases where analytic solutions of Poisson's equation exist are used to determine the accuracy of the solver. The implemented solver is found to be both efficient and accurate. Collisions are vitally important to the evolution of plasmas. The chemistry resulting from collisions is the reason why plasmas are so useful in technological applications. Electron collisions are included in the particle model using a Monte-Carlo technique. A basic method is given and several improvements are described. The most efficient combination of improvements is determined through a series of test cases. The error resulting from the collision selection process is characterised. Technological plasmas are formed from the electrical breakdown of a neutral gas. At atmospheric pressure the breakdown occurs as an electron avalanche. The particle model is used to simulate the nanosecond evolution of the avalanche from a single electron-ion pair. Special attention is paid to the inelastic collisions and the creation of metastables. The inelastic losses are used to estimate the photon emission from the electron avalanche. The Critical Ionisation Velocity phenomena is investigated using the particle model. When a neutral gas streams across a magnetised plasma the ionisation rate increases rapidly if the speed of the neutrals exceeds a critical value. Collisions between neutrals and positive ions create pockets of unbalanced negative charge. Electrons in these pockets are accelerated by their potential field and can reach energies capable of ionisation. The evolution of such an electron overdensity is simulated and their energy gain under different density and magnetic field conditions is calculated. The results from the simulation may explain the discrepancy between laboratory and space experiments.

Remapping (conservative interpolation), within arbitrary Lagrangian-Eulerian (ALE) schemes, requires the values of the scalar to be interpolated from one computational mesh to another which has differing geometry. Advection methods are typically utilised for the remapping stage, with fluxes being created by overlapping volumes between adjacent elements. In the thesis, a second-order, conservative, sign-preserving remapping scheme is developed utilising concepts of the Multidimensional Positive Definite Advection Transport Algorithm (MPDATA). The basic non-oscillatory and non-oscillatory infinite gauge options are derived for remapping in volume co-ordinates. For the first time, an MPDATA based remapping has been successfully implemented into full ALE schemes. Inherent properties of MPDATA are exploited to reduce wall heating errors via the second-order filtering option. The resulting increase in accuracy and symmetry of numerical solutions is demonstrated. For material interfaces, an adaptive mixed cell approach is proposed which takes advantage of the efficient computational stencil of MPDATA. The proposed approach utilises all available data in the calculation of pseudo velocities in MDPATA in order to retain second-order accuracy and multi-dimensionality at material interfaces. The effectiveness of the adaptive mixed cell approach is highlighted via examples featuring artificial material interfaces. Theoretical developments are supported by numerical testing. All test cases compare the accuracy of the MPDATA based schemes to a van Leer based scheme generalised to multiple dimensions via isotropic or Strang split remapping. The results demonstrate the advantages of the fully multi-dimensional MPDATA remapping.

The shallow water equations have been solved numerically using the Galerkin finite element method. Flow problems which can be classified as one-dimensional and two-dimensional are investigated. Two differing types of integration procedure (Gaussian Quadrature scheme and a mixed quadrature scheme involving both Gaussian Quadrature and Simpson's Rule) are examined to determine the most efficient way of obtaining the finite element solutions. The mixed quadrature scheme is shown to be a faster but less accurate process than the Gaussian scheme. The numerical results from the one-dimensional models are initially tested by comparison with the known analytic solutions for a straight channel and a wedge-shaped channel. Solutions from numerical models show good agreement with the analytic solutions. The one-dimensional models are also used to simulate the M₂ tide in the Bristol Channel. The results are in good agreement with observed field data. The two-dimensional models are tested against analytic solutions for a straight canal and an open coastal embayment with a variety of bottom topographies. The numerical results are in good agreement with the analytic solutions. Finite element solutions are found for real situations, in particular the area around Lundy Island within the Bristol Channel and in the Bristol Channel itself. The numerical solutions are compared with the observed field data. The two-dimensional numerical models produce solutions which are in good agreement with observed field data. An analysis of the eddy formation around Lundy Island shows that these features, which were first observed in satellite imagery, are predicted by the two-dimensional numerical models. Coriolis force is shown to be important in the formation of the island wake. The one-dimensional numerical models are less successful in predicting the observed field data than the two-dimensional numerical models but the former are very efficient in terms of computer time and also provide a good prediction of water levels and elevation phase lags.

This thesis investigates the interaction between soil and pipeline in sand subjected to lateral ground loading. The purpose of this study is to improve the structural modelling of buried pipelines; and also aims to produce design guidelines and construct normalised charts which will be of direct benefit to practising pipeline engineers. The research was performed entirely using the finite element (FE) method, and utilised the user subroutine of an advanced constitutive soil model that was implemented in this thesis. The problems examined in this research can be categorised into four main topics. First, 2-D FE analyses were conducted concerning with the effects of loading rate on a laterally-loaded pipeline buried in saturated sand. All indications support the conclusion that both the sand dilatancy and hydraulic conductivity of the soil in relation to the loading rate are important factors for mobilisation of the lateral resistance of a pipeline in a saturated soil medium. Second, soil loading on a pipeline under global soil shearing conditions was investigated by performing different types of relative ground and pipeline movement modes, with the aim of generating both passive and active failure states. Overall, it can be concluded that the effect of global soil shearing on the interaction of soil and pipeline is relatively small in terms of N_q, implying that local soil deformation and soil dilation characteristics are most important and influential factors contributing to the magnitude of the lateral pressure on pipelines. Third, investigations of the behaviour of an elbow-bend pipe, under lateral soil loading were performed using a 3-D FE modelling method. It was found that deeper burial pipeline, denser soil and elbow-bend pipe with larger bending angle accounted higher N_q. Also N_q at the elbow-bend pipe was about 2.7 times higher than a straight pipe. The results confirmed that the ‘3-D elbow effect’ can be ignored in the closing mode case, but in the opening mode case, the effect was computed at about 17% when compared to a 2-D bilinear soil-spring model case. Additionally, a larger effective plastic strain region was observed when 3-D soil-spring models were adopted in the design. Fourth, in order to achieve a reliable design procedure against permanent ground deformation (PGD), a full-scale 3-D FE numerical analysis and a full-scale 3-D spring model analysis were both carried out on a 90° elbow pipeline. Encouraging and good results were achieved from both of the numerical models when compared with the data from experiments carried out at Cornell University. Thus, it is shown that the adopted 3-D FE method was able to simulate the observed pipeline performance under PGD ground failure in a reliable way.

This thesis uses numerical simulations to assess the most suitable model type for simulating dispersive and non dispersive tsunami wave propagation over a range of bathymetries. These simulations are presented in two parts. The first part highlights differences between results as predicted by a fully nonlinear Boussinesq model (with its ability to predict dispersion) and a non dispersive, linear or weakly nonlinear model, for simulations of a dispersive wave incident at various idealized bathymetric features. The second part determines the efficacy in a real world application of the Boussinesq model as opposed to a nonlinear shallow water model. In addition, a discussion on the geophysical parameters which influence the choice of numerical model for simulating tsunami propagation in a particular bathymetric region is provided.

This thesis is based on the application of hydraulic modelling techniques to the study of river rehabilitation schemes. River channelization and rehabilitation techniques are reviewed and the restoration of the River Idle is detailed. The rehabilitation of the Idle, consisting principally of the installation of a number of flow deflectors, forms the basis of the modelling work carried out. Open channel modelling techniques are reviewed and the packages ISIS, HEC-RAS, SSIIM and CFX are applied to the River Idle. Results from SSIIM (two dimensional) and CFX (three dimensional) are validated against site measured velocities. SSIIM predicted velocities calibrate poorly against site data whilst CFX results are considerably more encouraging. Reasons for the increased accuracy of the three dimensional results are discussed. The effect of the installation of the flow deflectors on aquatic habitat is simulated using the techniques underlying the Instream Flow Incremental Methodology (IFIM). The results from the one dimensional model ISIS and the three dimensional package CFX are used to make available habitat predictions. Results indicate an improvement in habitat for adult and spawning chub but a worsening of habitat for roach fry. However, habitat for roach fry can be expected to improve with time as the geomorphology of the river responds to the installation of the deflectors. The results from the habitat modelling exercise also indicate significant discrepancies between the results obtained by applying the one and three dimensional models. Greater improvements in habitat are indicated in the results from the three dimensional modelling approach. This can be attributed to a number of factors but most significantly the fact that the three dimensional model, in solving two further momentum balance equations, accurately simulates a plume of higher velocity which is produced by the narrowing of the channel width at the deflector. This plume of higher velocity is propagated downstream for some distance beyond the deflector and is associated with improved habitat suitability in the case of adult and spawning chub. The effect of the deflectors on the movement of sediments in the Idle is simulated using ISIS Sediment, a module of the ISIS package, and SHEAR. SHEAR is a FORTRAN program, written for this thesis, which calculates bed shear stresses from the vertical velocity distribution predicted by CFX. The predicted bed shear stresses are compared with a critical shear stress for erosion which is calculated from the Shields criteria. Deposition areas can be implied from zones of reduced bed shear stress. Thus, SHEAR is able to describe the spatial detail of erosion and deposition, for any given sediment particle size, at a specific discharge. Results from ISIS Sediment and SHEAR are compared qualitatively with site measurements of bed erosion that has taken place at a single deflector site. Results indicate that the programs have successfully reproduced the major features of the movement of sediments observed on site. These consist of the erosion of a scour pool adjacent to the deflector tip and deposition in the lee of the deflector leading to the development of a bank of sediment. Overall, significant benefits are indicated in a three dimensional approach over the more traditional one dimensional models. These are evident in both improved calibration with site measured velocities, better available habitat prediction and the ability to describe the spatial detail of erosion and deposition.

Most physical problems involving viscous fluid flows are characterized by turbulence where instabilities and large velocity gradients generate fluctuations in the flow field. Towed sonar arrays are exposed to turbulence in the boundary layer formed around the cable. Problems are related to the cable rotating around its own axis due to variations in tension force caused by the towing vehicle. Numerical calculations of a pressure driven flow along a cylinder are performed for the purpose of investigating the turbulent boundary layer around the cable. In this study, the numerical software OpenFOAM has been used in order to solve the flow field. The Reynolds Average Navier-Stokes (RANS) approach was applied, providing a time-average solution of the flow quantities. The results were used in a comparative study with data obtained from Large Eddy Simulation (LES). Simulations were carried out for two Reynolds numbers based on the shear velocity; Re_tau=[240,550]. The cylinder was assigned two different rotational velocities in addition to a case with zero rotation. Results show that the normalized mean velocity profile is in good agreement with the universal law-of-the-wall and previous published data. Comparison with LES data indicated good agreement with Reynolds shear stresses and the normalized mean velocities in the case of a non-rotating cylinder. However, deviations were observed when rotation was applied. In order to ensure the quality of the numerical results a convergence study was performed. Special attention was paid to the near-wall region in order to capture all levels of the boundary layer.

This thesis examines the numerical representation of stable minimal surfaces. In particular, the work presented concentrates on the formulation of a finite element, suitable for the analysis of systems subjected to large strains and large displacements. In order to obtain an understanding of the physical properties of a minimal surface, and to verify the proposed numerical solution algorithms, the surfaces developed by several soap-film models are given. The mechanisms involved in the formation of a soap-film (minimal) surface is summarised. Several types of minimal surfaces are investigated, including general surfaces between rigid boundaries, single minimal surfaces between two frames, and those with internal and external flexible boundaries. In addition, the question of the stability of minimal surfaces is discussed, in terms of a finite and an infinitesimal perturbation. The numerical modelling of minimal surfaces is presented, based initially on the discretisation of the form using plane linear (line) and triangular elements. The application of the matrix-based element formulations to the vector-based Dynamic Relaxation solution algorithm is described. The formulations of the elements are assessed in the context of large strains and large displacements. Subsequently, the effects of the violations of the assumptions inherent in the derivation of the element stiffness matrices on the accuracy of the numerical solution are demonstrated, and measures proposed to maintain the stability of the solution algorithm. The numerical solutions to several minimal surfaces are provided, based on the linear and triangular element discretisations respectively. An intended improvement on the plane linear and triangular element formulations is proposed by the derivation of a higher order finite element. A 24 degrees-of-freedom finite element is formulated, representing a general curved elastic (or inelastic) geometrically non-linear continuum, and modelling the condition of plane stress. The element equations are derived with special consideration of the simulation of the effects of large strains and large displacements. An appraisal of the quality of the element formulation is made through the application of the Patch test and the Eigenvalue test. The solutions to several minimal surfaces are presented, from which the effects of the assumptions in the element formulation on the accuracy of the proposed numerical solution algorithm are demonstrated.

Adapting to climate change is one of the greatest challenges facing engineers. Many studies have been conducted since the 1900s directed at predicting extreme weather events. Changes in global weather patterns, such as temperature and rainfall distributions, can have major economic and societal impacts. One example, addressed in this thesis, is the stability of natural slopes. In Southeast Asia, landslides are common due to the effect of abundant rainfall during the wet monsoon. The local climate in the region is characterised by annual wet and dry seasons, in which the cycle forms an unsaturated zone at the surface of the slopes. However, as a result of climate change, prolonged drying and heavy rainfall are observed that may exacerbate slope failure particularly in unsaturated soils. The prediction and mitigation of slope failures are consequently major challenges due to the complexity of the unsaturated behaviour of tropical soils subjected to irregular weather changes. This thesis develops a methodology to model unsaturated slope behaviour taking into account the effects of climate change. The approach includes groundwater flow, soil deformation and stability analyses using a finite element method and climate change predictions to incorporate future weather scenarios. The method was established by validating the groundwater flow analysis by involving a case study in Zaoyang, China. Subsequently, a more complex case study of a tropical unsaturated slope in Bukit Timah, Singapore was also considered to calibrate the soil-water characteristic curves (SWCC), a major controlling factor in unsaturated soils mechanics. The coupled flow-deformation analysis was undertaken on the validated case studies to predict soil displacement. In addition, a parametric study was conducted to critically analyse the effects of void ratio, saturated permeability, hysteretic SWCC, soil elasticity and rainfall intensity regarding slope behaviour. Finally, statistical analysis was performed to predict the impact of climate change on the rainfall distribution in Singapore up to the year 2100 by using the historical data from 1980 to 2010. Frequency analysis was adopted to estimate the rainfall return period. The results of the future extreme rainfall were compared to predictions by the Met Office in Singapore and the United Kingdom. The effects of climate change on slope behaviour was assessed by applying the predicted climate in the slope models. The outcomes reveal that the modelling approach is able to capture groundwater flow, slope deformation and safety factor accurately under extreme weather scenarios.

A finite difference computational model has been enhanced and refined to simulate tide-induced circulatory flows, with special reference to eddies shed in the lee of headlands and tidal circulation and flushing in narrow entranced coastal basins. The model is of the two-dimensional depth-integrated type and includes a relatively simple "zero-equation" turbulence model. In the turbulence model particular emphasis has been placed on the representation of the free shear layer turbulence, occurring in the mixing zone of eddying flows. This component of turbulent structure has been expressed in terms of a constant eddy viscosity across the shear layer and a semi-empirical velocity distribution. The finite difference representation of the hydrodynamic and mass transport equations was based on the Alternating Direction Implicit scheme, with the hydrodynamic equations involving a double iteration to represent the advective acceleration terms in a time-centred form. The solution of the governing equations yielded the depth-mean velocity, water elevation and concentration fields throughout the computational domain.The model's ability to simulate tide-induced circulatory flows was tested against field measurements from around Rattray Island, and laboratory model studies of idealised rectangular harbours. The agreement between numerical predictions and measurements proved to be encouraging in both cases. The one-way interaction nesting technique has been adopted and applied with success to the harbour simulations. A final application of the numerical model to prototype harbours, enabled comparisons to be made between prototype and laboratory model predictions, an exercise which highlighted the problems associated with scaling effects in distorted physical models.

The aim of this research project is to provide the academic and industrial community with a numerical tool that can be used for describing extreme flow cavitation scenarios and the atomisation process of these multiphase jets in a low-pressure environment. The research lies in the intersection of Numerical Analysis, Applied Physics and programming. From the physical point of view, the project has two different strands: The first is developing a methodology for channel flows due to a rapid pressure drop which is possible to result into various flow regimes inside the channel. The second step is to track the liquid fragmentation of the liquid jet downstream the channel exit and describing the atomisation process to liquid ligaments and blobs to droplets. Using a fully Eulerian approach, this research aims towards a holistic approach that addresses some of the major challenges that govern superheated jets atomisation. The finite volumes method in a compressible framework is used utilising various models for modelling the underpinning physics of flashing jets. Flashing occurs either if a liquid follows an isothermal depressurisation or isobaric heating. In both cases, the fluid fails to adjust to the local changes in pressure and temperature admitting a metastable state which makes the process more challenging to understand. The Homogeneous-Relaxation-Model (HRM) is used for modelling the heat transfer under sudden depressurisation conditions accounting for the non-equilibrium vapour generation. A new pressure equation is proposed which employs the continuity equation indirectly. The pressure responds to compressibility and density changes due to the rapid phase change and includes the surface tension contribution in the pressure-velocity coupling algorithm. The coupling of the continuity and momentum equation with the HRM and the interface tracking method is thoroughly described. The result of this coupling is a conserved numerical method that is capable of characterising the flow regimes and the impact of bubble nucleation on the mass flow rate. The present study presents a numerical approach for simulating the atomisation of flashing liquids accounting for the distinct stages, from primary atomisation to secondary break-up to small droplets Following the Eulerian-Lagrangian-Spray-Atomisation approach, the concept of the surface density Σ is introduced into the methodology for the spray dynamics. The proposed approach has the advantage of avoiding the unrealistic common assumption of pure liquid at the nozzle exit. It models the change in the regime inside the nozzle treating flashing in a unified approach simulating the metastable jet both inside and outside the nozzle. Important mechanisms such as thermal non-equilibrium, aerodynamic break-up, droplet collisions and evaporation are modelled in a novel atomisation model. The modified Σ- equation employed a new source term proposed for cryogenic jets. A wide range of numerical tests is presented for validation and obtaining insights for the underlying physics. Short and long nozzle geometries are tested for both low and high-pressure releases for flashing water, R134A, liquid nitrogen and LNG. Results for turbulent flows for both sub-cooled and superheated liquids are presented showing that the proposed approach can accurately simulate the primary atomisation.

Finite difference numerical methods are developed for the solution system in the biomedical sciences; namely, fox-rabies model. First-order methods and second-order method are developed to solve the fox-rabies equations. The fox-rabies model is extended to one-space dimension to incorporate diffusion. The reaction terms in these systems of partial differential equations contain non-linear expressions. It is seen that the numerical solutions are obtained by solving non-linear algebraic system at each time step, as opposed to solving anon-linear algebraic system which is often required when integrating non-linear partial differential equations. The numerical methods proposed for the solution of the initial-value problem for the fox-rabies model are characterized to be implicit. In each case, however, it seen that the numerical solutions are obtained explicitly. In a series of numerical experiments, in which the ordinary differential equations are solved first of all, it seen that the proposed methods have an identical stability properties to those of the well-known, first-order, Euler method. The proposed methods for the numerical solution of partial differential equations are seen to be economical and reliable. Error analysis for the methods, computer implementation and numerical results are discussed. The stability of the numerical method is analyzed using maximum principle analysis.

Bibliography: pages 107-110.
Aluminium forms a highly neurotoxic complex with maltol (3-hydroxy-2-methyl-4H-pyran-one). The stability of this complex has been determined using glass-electrode potentiometry. Owing to the effect on nuclear relaxation behaviour, paramagnetic contrast agents have immense diagnostic potential and have recently received a great deal of attention in the literature. The gadoliniummaltol complex was studied with the view to developing a potential tissue-specific magnetic resonance imaging contrast agent. Because of the interest in medical applications of radioactive isotopes of group 1118 elements, the indium-maltol complex was studied in order to assess its radiopharmaceutical usefulness. The major analytical techniques used in this study are potentiometry and high resolution nuclear magnetic resonance spectroscopy.

Landfast sea ice is a recurring seasonal feature along many coastlines in the polar regions. It is characterised by a lack of horizontal motion, for at least 20 days, and its attachment to the coast or seabed. It can form as a result of restrictive geometry, such as channels or embayments, or through the grounding of thick ice ridges which add lateral stability to the ice cover. Due to its stationary and persistent nature, landfast ice fundamentally modifies the exchange of heat and momentum between the atmosphere and ocean, compared with more mobile pack ice. The current generation of sea ice models is not capable of reproducing certain aspects of landfast ice formation and breakup. In this work two landfast ice parameterisations were developed, which describe the formation and breakup of landfast ice through the grounding of thick ice ridges. The parameterisations assume the sub-grid scale distribution of ice draft and ocean depth, the two parameters important in determining the occurrence of grounded ridges. The sub-grid scale distribution of grounded ice is firstly defined by assuming that ice draft and ocean depth are independent. This parameterisation allowed ice of any thickness to occur and ground at any depth. Advancing from this the sub-grid scale distribution of the grounded ice was restricted in an effort to make it more realistic. Based on Arctic ice scour observations ice was prevented from grounding in regions where the draft thickness was much larger than the ocean depth. Both parameterisations were incorporated into a commonly used sea ice model, the Los Alamos Sea Ice Model (CICE), to which a multi-category ocean depth distribution from high resolution global bathymetry data (ETOPO1) was included. The parameterisations were tested in global standalone format (i.e. no active ocean) with realistic atmospheric forcing. Both parameterisations were found to improve the spatial distribution and the seasonal cycle of landfast ice compared to the control (i.e. no landfast ice parameterisation) in the Arctic and Antarctic. However, the grounded ridges produced by the parameterisations were very stable, and tended to become multiyear leading to the production of multiyear landfast ice, which was particularly widespread in the Antarctic. It was found that tides have a significant impact on both grounded and landfast ice. In some polar locations tides were found to increase the occurrence of landfast ice, by increasing the production of thick ridges which were able to ground. Conversely, in some regions, tides were found to decrease the occurrence of landfast ice, as strong tidal and residual currents increased the mobility of the grounded ridges and landfast ice. This thesis finishes by considering whether a sea ice model could be used to further our understanding of the physical landfast ice system. Analytically derived characteristic numbers, which describe the ability of landfast ice to form, were found to fully describe the formation of landfast ice within the sea ice model CICE during idealised 1D scenarios. For these scenarios the key parameters controlling ice motion were found to be the external forcing component, the width of the ice cover, the internal ice strength, and the thickness of the ice. However, an exact characteristic variable able to describe the occurrence of landfast ice in an idealised 2D scenario could not be found analytically, nor could it be inferred numerically, and this remains an area for further research. This thesis examines different methods of modelling landfast sea ice and provides the sea ice modelling community with a means to parametrise landfast ice formation as a result of grounded ridges without having to work at very fine resolution, as this is computationally inefficient.

The centrifugal casting process is a common method for manufacturing the tubes, etc. Due to its high temperature and invisible mold, it is really difficult to know the mechanism of molten steel inside the mold. It is important to know the mechanism of the molten steel inside mold, since it will help the manufacturer to know more accuracy of the flow of the molten steel so that it can work for improving the productivity and quality of the products. Casting funnel design is the designed by Åkers for their funnel which will result in different flow behavior. In thesis work, casting funnel design will be investigated so that it can make sure that the casting funnel design can affect the flow behavior of molten steel or not. Another method of changing the diameter of nozzle was also carried out and investigated with both simulation and experiment to changing flow behavior of molten steel. It will give Åkers alternative method for changing the flow behavior to liquid steel. The mechanism of solidification in centrifugal casting is also really important since it can give manufacturer the general view of solidification process. So solidification of centrifugal casting is also investigated in the thesis work.

Shotcrete is a special type of concrete which was invented at the beginning of the 20th century and is nowadays an important support element for tunnels constructed with the New Austrian Tunnelling Method (NATM). Immediately after tunnel excavation shotcrete is sprayed onto the tunnel walls at high pressure in order to provide temporary support. Unfortunately, in the past very little attention has been given to the development of sophisticated material laws for shotcrete, since its design and application was mainly based on experience. However, current design practice, such as that applied in the design of the new Crossrail tunnels, requires sophisticated modelling of shotcrete behaviour in numerical analysis of tunnel-soil interaction. Such models are not readily found in the literature, as they have been developed mainly for structural, rather than geotechnical applications. In this thesis, a constitutive model for the time-dependent behaviour of shotcrete has been developed within the framework of elasto-plasticity. Two independent yield surfaces control the behaviour of shotcrete in multiaxial loading conditions for both compression and tension. The model formulation is based on strain hardening/softening plasticity, where the expansion and contraction of the yield surfaces are governed by normalised plastic strains. Cracking of the shotcrete is considered within the smeared crack concept. Furthermore, the proposed material law includes the time-dependency of stiffness and strength behaviour. The reducing deformability of the shotcrete during cement hydration has been taken into account. The model has been extended to account for creep, shrinkage and hydration temperature induced deformations at early shotcrete ages. After a robust implementation into the Imperial College Finite Element Program (ICFEP), model calibration and validation have been performed for shotcrete experiments taken from the literature. The developed constitutive model has then been applied to the analysis of a typical tunnel construction in London Clay, modelling the early age material properties of the shotcrete tunnel lining in detail for various excavation schemes. Finally, it has been shown that the proposed constitutive model is capable of reproducing the complex behaviour of young shotcrete at early ages and can be applied successfully to boundary value problems in geotechnical engineering.

The increase in computational power in the last 20 years has made it feasible to solve the full Stokes equation for ice flow, using finite element methods (FEM). However, the numerical properties of these equations remains largely unknown. This is due to their nonlinear nature, which makes them hard to analyze mathematically. For this reason convergence rate and stability has to be established by performing simulations. In this thesis a 2D ice solver has been developed. The solver was then tested on the ISMIP-HOM benchmarks, in order to assert convergence rates and stability. The solver was developed using the FEM software FEniCS. It was verified that the solver could obtain the same convergence rate as in the case of linear Stokes; however, for curved boundaries the convergence rate in velocity dropped by one order. It was also found that discontinuity in the coefficient of basal traction reduced convergence rate to linear in both pressure and velocity. Time dependence was added to the solver by coupling the Stoke's system to the kinematic free surface equation. Time dependence was then tested using one of the EISMINT benchmark. It was found that for a mesh with a mesh size parameter of 10 km, instabilities arised after 2500 years when using a time step of 25 years, resulting in spurious numerical oscillation. However, by introducing a diffusive term into the surface equation, it was possible to attenuate these oscillation without affecting the overall shape of the ice sheet.

The numerical modelling of electromagnetic waves has been the focus of many research areas in the past. Some specific applications of electromagnetic wave scattering are in the fields of Microwave Heating and Radar Communication Systems. The equations that govern the fundamental behaviour of electromagnetic wave propagation in waveguides and cavities are the Maxwell's equations. In the literature, a number of methods have been employed to solve these equations. Of these methods, the classical Finite-Difference Time-Domain scheme, which uses a staggered time and space discretisation, is the most well known and widely used. However, it is complicated to implement this method on an irregular computational domain using an unstructured mesh. In this work, a coupled method is introduced for the solution of Maxwell's equations. It is proposed that the free-space component of the solution is computed in the time domain, whilst the load is resolved using the frequency dependent electric field Helmholtz equation. This methodology results in a timefrequency domain hybrid scheme. For the Helmholtz equation, boundary conditions are generated from the time dependent free-space solutions. The boundary information is mapped into the frequency domain using the Discrete Fourier Transform. The solution for the electric field components is obtained by solving a sparse-complex system of linear equations. The hybrid method has been tested for both waveguide and cavity configurations. Numerical tests performed on waveguides and cavities for inhomogeneous lossy materials highlight the accuracy and computational efficiency of the newly proposed hybrid computational electromagnetic strategy.

The main focus of this thesis is to provide efficient modelling and optimization strategies for a certain electro-magnetic device known as magnetic gear. In particular, magnetic, thermal and mechanical models are discussed and the non-linear material models are examined, including permanent magnets demagnetization algorithms and hysteresis models in laminated sheets. From the magnetic modelling point of view, an analytic approach for the initial simplified gear design is presented. A special focus is given to the computational burden of the method that is especially tailored for stochastic optimization procedures. For the detailed analysis of magnetic gears, an algorithm based on Finite Element / Boundary Element coupling is proposed, including ferromagnetic non-linearities, mechanical ordinary differential equations, eddy currents and circuit equations. Detailed models are introduced and discussed to analyze the effects of soft material hysteresis and permanent magnets magnetization, demagnetization and recoil. Loss mechanisms in magnetic gears are also investigated, and the transmission losses at varying rotational speeds and load angles are analyzed. A simplified mechanical model of the magnetic gear is presented and formulated as a set of inequality constraints, thus giving a direct link to optimization strategies. The mechanical constraints include the iron poles displacements and stresses and the limitations on the rotational speed due to excessive stresses, resonances and vibrations. A simplified analysis based on an equivalent thermal network is also presented, where the axial cooling flux is also considered. Stochastic optimization techniques are discussed for a multi-physic optimized machine design, and the analytic model is embedded in a Differential Evolution scheme. Finally, the optimized results are discussed and compared to commercial mechanical gearboxes. A solution based on the stiffness rods connection is also proposed and analyzed to provide a damping effect when the gear operation becomes asynchronous. During the PhD, there has been a constant effort aimed at building a prototype for the validation of the numerical models but, for different reasons, none of the manufacturers finalized the project. Thus, all the algorithms have been validated by comparing their output with commercial codes or, when possible, with data from experiments retrieved from literature. Because of this reasons and since the major objective of this thesis regards the numerical techniques for magnetic gears simulation, different magnetic transmissions have been adopted as numerical test cases for the validation of the algorithms.
L'obiettivo principale di questa tesi è quello di fornire strategie di modellazione e ottimizzazione efficienti per un dispositivo elettromagnetico noto come ingranaggio magnetico. In particolare modelli magnetici, termici e meccanici sono esaminati includendo materiali non lineari, algoritmi di smagnetizzazione magneti permanenti e modelli di isteresi in nuclei laminati. Dal punto di vista della modellazione magnetica, un approccio analitico per la progettazione semplificata dell'ingranaggio è presentata. Particolare attenzione viene data all'onere computazionale del metodo che è particolarmente adatto alle procedure di ottimizzazione stocastica. Per l'analisi dettagliata degli ingranaggi magnetici, un algoritmo basato sull'accoppiamento Finite Element / Boundary Element viene proposto, comprese le non linearità ferromagnetiche, le equazioni differenziali meccaniche, correnti parassite ed equazioni circuitali. Modelli dettagliati sono introdotti e discussi per analizzare gli effetti dell'isteresi dei materiali dolci e magnetizzazione, smagnetizzazione e recoil di magneti permanenti. Vengono anche investigati i meccanismi di perdita negli ingranaggi magnetici e le perdite di trasmissione al variare delle velocità di rotazione e gli angoli di carico. Un modello meccanico semplificato dell'ingranaggio magnetico è presentato e formulato come un insieme dei vincoli di disuguaglianza, fornendo così un collegamento diretto alle strategie di ottimizzazione. I vincoli meccanici includono gli spostamenti e le sollecitazioni dei poli ferromagnetici e le limitazioni sulla velocità di rotazione dovuta a sforzi eccessivi, risonanze e vibrazioni. Un'analisi semplificata basata su una rete termica equivalente è presentato, nella quale si considera anche il flusso di raffreddamento assiale. Le tecniche di ottimizzazione stocastica sono discusse per una progettazione multi-fisica della macchina ottimizzata e il modello analitico è incorporato in uno schema di evoluzione differenziale. Infine, i risultati ottimizzati sono discussi e confrontati con le soluzioni meccaniche commerciali. Viene inoltre proposta e analizzata una soluzione basata sulla connessione delle barre assiali che garantiscono un effetto di smorzamento quando la marcia dell'ingranaggio diventa asincrona. Tutti gli algoritmi sono stati convalidati tramite confronto con codici commerciali o, quando possibile, con i dati di esperimenti recuperati dalla letteratura.

Soft materials have a wide range of applications, which include the production of masks for nano–lithography, the separation of membranes with nano–pores, and the preparation of nano–size structures for electronic devices. Self–organization in soft matter is a primary mechanism for the formation of structure. Block copolymers are long chain molecules composed of several different polymer blocks covalently bonded into a single macromolecule, which belong to an important class of soft materials which can self–assemble into different nano–structures due to their natural ability to microphase separate. Experimental and theoretical studies of block copolymers are quite challenging and, without computer simulations, it is difficult and problematic to analyse modern experiments. The Cell Dynamics Simulation (CDS) technique is a fast and accurate computational technique, which has been used to investigate block copolymers. The stability has been analysed by making use of different discrete Laplacian operators using well–chosen time steps in CDS. This analysis offers stability conditions for phase–field, based on the Cahn–Hilliard Cook (CHC) equations of which CDS is the finite difference approximation. To overcome grid related artefacts (discretization errors) in the computational grid, the study has been done for employing an isotropic Laplacian operator in the CDS framework. Several 2D and 3D discrete Laplacians have been quantitatively compared for their isotropy. The novel 2D 9–point BV(D2Q9) isotropic stencil operators have been derived from the B.A.C. van Vlimmeren method and their isotropy measure has been determined optimally better than other exiting 2D 9–point discrete Laplacian operators. Overall, the stencils in 9–point family Laplacians in 2D and the 19–point stencil operators in 3D have been found to be optimal in terms of isotropy and time step stability. Considerable implementation of Laplacians with good isotropy has played an important role in achieving a proper structure factor in modelling methods of block copolymers. The novel models have been developed by implementing CDS via more stable implicit methods, including backward Euler, Crank–Nicolson (CN) and Alternating Direction Implicit (ADI) methods. The CN scheme were implemented for both one order and two order parameter systems in CDS and successful results were obtained compared to forward Euler method. Due to the implementation of implicit methods, the CDS has achieved second–order accuracy both in time and space and it has become stronger, robust and more stable technique for simulation of the phase–separation phenomena in soft materials.