The monitoring and assessment of prawn populations in New South Wales (NSW), Australia, has been identified as a continuing research priority by both the fishing industry and the fisheries managers. This dissertation presents a series of dynamic population models developed to evaluate the status of the eastern king prawn (Melicertus plebejus) and eastern school prawn (Metapenaeus macleayi) populations within NSW and to analyse the relative performance of a number of alternative management strategies involving the three fisheries that target these species. Monthly commercial prawn catch and effort data from 1984 to 2006 were used to calibrate the stock assessment models. Where possible, the results of previous research were used to develop the structure of the model and to provide estimates of biological parameters. A process of increasing model complexity, including the addition of physical processes, such as river discharge events and economic considerations, was undertaken in an attempt to develop the most appropriate model for the analysis of management strategies. The first model presented was used to undertake a single-species assessment of the eastern king prawn stock and was based on a delay-difference population model with four different representations of recruitment. This model was calibrated to observations using the Bayesian sampling/importance re-sampling method and used to test the effect of significant changes in the future catch on the stock. The second model presented is a size-based metapopulation model which incorporated the dynamics of school prawns over three habitats, being harvested by three different fishing methods. This model was used to test the effect of alternative climate variability scenarios on the stock. The third model presented is a multi-species, multi-fishery bio-economic model. This model was used to examine the impact of nine alternative economic scenarios, incorporating various combinations of input costs and product prices. The results from the use of these models indicated that neither of the prawn population appeared to be over-exploited. The analyses also indicated that none of the alternative management strategies were found to stand-out enough to justify a move away from the current management strategy of input controls and spatio-temporal closures, even under a range of future scenarios including climate change and large movements in input costs and product prices.

The modelling of the processes of advection and dispersion-diffusion is the most crucial factor in solute transport simulations. It is generally appreciated that the first order upwind difference scheme gives rise to excessive numerical diffusion, whereas the conventional second order central difference scheme exhibits severe oscillations for advection dominated transport, especially in regions of high solute gradients or discontinuities. Higher order schemes have therefore become increasingly used for improved accuracy and for reducing grid scale oscillations. Two such schemes are the QUICK (Quadratic Upwind Interpolation for Convective Kinematics) and TOASOD (Third Order Advection Second Order Diffusion) schemes, which are similar in formulation but different in accuracy, with the two schemes being second and third order accurate in space respectively for finite difference models. These two schemes can be written in various finite difference forms for transient solute transport models, with the different representations having different numerical properties and computational efficiencies. Although these two schemes are advectively (or convectively) stable, it has been shown that the originally proposed explicit QUICK and TOASOD schemes become numerically unstable for the case of pure advection. The stability constraints have been established for each scheme representation based upon the von Neumann stability analysis. All the derived schemes have been tested for various initial solute distributions and for a number of continuous discharge cases, with both constant and time varying velocity fields. The 1-D QUICKEST (QUICK with Estimated Streaming Term) scheme is third order accurate both in time and space. It has been shown analytically and numerically that a previously derived quasi 2-D explicit QUICKEST scheme, with a reduced accuracy in time, is unstable for the case of pure advection. The modified 2-D explicit QUICKEST, ADI-TOASOD and ADI-QUICK schemes have been developed herein and proved to be numerically stable, with the bility sta- region of each derived 2-D scheme having also been established. All these derived 2-D schemesh ave been tested in a 2-D domain for various initial solute distributions with both uniform and rotational flow fields. They were further tested for a number of 2-D continuous discharge cases, with the corresponding exact solutions having also been derived herein. All the numerical tests in both the 1-D and 2-D cases were compared with the corresponding exact solutions and the results obtained using various other difference schemes, with the higher order schemes generally producing more accurate predictions, except for the characteristic based schemes which failed to conserve mass for the 2-D rotational flow tests. The ADI-TOASOD scheme has also been applied to two water quality studies in the U. K., simulating nitrate and faecal coliform distributions respectively, with the results showing a marked improvement in comparison with the results obtained by the second order central difference scheme. Details are also given of a refined numerical representation of flooding and drying of tidal flood plains for hydrodynamic modelling, with the results showing considerable improvements in comparison with a number of existing models and in good agreement with the field measured data in a natural harbour study.

The monitoring and assessment of prawn populations in New South Wales (NSW), Australia, has been identified as a continuing research priority by both the fishing industry and the fisheries managers. This dissertation presents a series of dynamic population models developed to evaluate the status of the eastern king prawn (Melicertus plebejus) and eastern school prawn (Metapenaeus macleayi) populations within NSW and to analyse the relative performance of a number of alternative management strategies involving the three fisheries that target these species. Monthly commercial prawn catch and effort data from 1984 to 2006 were used to calibrate the stock assessment models. Where possible, the results of previous research were used to develop the structure of the model and to provide estimates of biological parameters. A process of increasing model complexity, including the addition of physical processes, such as river discharge events and economic considerations, was undertaken in an attempt to develop the most appropriate model for the analysis of management strategies. The first model presented was used to undertake a single-species assessment of the eastern king prawn stock and was based on a delay-difference population model with four different representations of recruitment. This model was calibrated to observations using the Bayesian sampling/importance re-sampling method and used to test the effect of significant changes in the future catch on the stock. The second model presented is a size-based metapopulation model which incorporated the dynamics of school prawns over three habitats, being harvested by three different fishing methods. This model was used to test the effect of alternative climate variability scenarios on the stock. The third model presented is a multi-species, multi-fishery bio-economic model. This model was used to examine the impact of nine alternative economic scenarios, incorporating various combinations of input costs and product prices. The results from the use of these models indicated that neither of the prawn population appeared to be over-exploited. The analyses also indicated that none of the alternative management strategies were found to stand-out enough to justify a move away from the current management strategy of input controls and spatio-temporal closures, even under a range of future scenarios including climate change and large movements in input costs and product prices.

Research Doctorate - Doctor of Philosophy (PhD) / Due to the effects of global warming and climate change there is currently intense and growing international interest in suitable modelling methods for relating satellite remotely sensed spectral imagery of vegetated landscapes to the biophysical structural variables in those landscapes across regional, continental or global scales. Of particular interest here is the satellite optical remote sensing of forest foliage cover—measured as foliage projective cover (FPC)—by Landsat ETM+ (Enhanced Thematic Mapper plus) sensor. In the remote sensing literature, different empirical and physical modelling approaches exist for relating remotely sensed imagery to the landscape parameters of interest, each with their own advantages and disadvantages. These approaches, in the main, may be broadly categorised as belonging to one, or a combination of: spectral mixture analysis (SMA) modelling, canopy reflectance modelling, multiple regression (MR) modelling or, spectral vegetation index (SVI) modelling. This thesis uses the SVI approach, partly in comparison to the MR approach. Both the SVI and MR approaches require field-based data to establish the relationship between the biophysical parameter and the spectral index or spectral responses within defined spectral bandwidths. Surrogate measures of the biophysical parameter are sometimes used extensively to establish this relationship and therefore a separate calibration relationship is required.This has inherent problems when the output of one model is substituted into the next and the effects of carry-over of error from one model to the next are not considered. My main goal is therefore to develop a modelling approach that will allow a larger set of one or more surrogate measures to be combined with a smaller set of ‘true’ measures of the biophysical parameter into the one model for establishing the relationship with the SVI and hence the spectral imagery. Success in meeting the goal is the illustration of a working model using real data. In progression towards meeting the goal, two new modelling ideas are developed and synthesised into the creation of an overall modelling framework for estimating FPC from spectral imagery. The modelling framework, which has potential for use in other applications, allows for the incorporation of different types of data including different calibration relationships between variables while avoiding the usual, stepwise approach to the linking of separate relationship models and their variables. One contribution that is new to both remote sensing and statistical modelling practices involves a polar transformation of the principal components of a multi-spectral image of a local reference landscape to produce a set of empirically based, invariant three-dimensional spectral index transformations that have potential for application to the spectral images of different regional landscapes and possibly global landscapes. In particular, the vegetation index from the set has approximate bounded properties that we exploit for modelling of its contribution to residual variation in its relationships with the biophysical variables measured on the ground. The other contribution to statistical modelling practice that has potential for application by a wide range of disciplines is the direct modelling of interdependent relationships between pairs of bounded variates, each considered to have a measurement error structure that can be modelled as though it is similar to sampling variation. Associated with this particular contribution is the development of novel geometric methods to construct approximate prediction bounds and to assist with model interpretations.

A novel higher-order moment-closure method is applied for the Eulerian treatment of gas-particle multiphase flows characterized by a dilute polydisperse and polythermal particle phase. Based upon the polydisperse Gaussian-moment model (PGM) framework, the proposed model is derived by applying an entropy-maximization moment-closure formulation to the transport equation of the particle-number density function, which is equivalent to the Williams-Boltzmann equation for droplet sprays. The resulting set of first-order robustly-hyperbolic balance laws include a direct treatment for local higher-order statistics such as co-variances between particle distinguishable properties (i.e., diameter and temperature) and particle velocity. Leveraging the additional distinguishing variables, classical hydrodynamic droplet evaporation theory is considered to describe unsteady droplet vaporization. Further, studying turbulent multiphase flow theory, a first-order hyperbolicity maintaining approximation to turbulent flow diffusion-inertia effects is proposed. Investigations into the predictive capabilities of the model are evaluated relative to Lagrangian-based solutions for a range of flows, including aerosol dispersion and fuel-sprays. Further, the model is implemented in a massively parallel discontinuous-Galerkin framework. Validation of the proposed turbulence coupling model is subsequently performed against experimental data, and a qualitative analysis of the model is given for a qualitative liquid fuel-spray problem.

The modelling of the processes of advection and dispersion-diffusion is the most crucial factor in solute transport simulations. It is generally appreciated that the first order upwind difference scheme gives rise to excessive numerical diffusion, whereas the conventional second order central difference scheme exhibits severe oscillations for advection dominated transport, especially in regions of high solute gradients or discontinuities. Higher order schemes have therefore become increasingly used for improved accuracy and for reducing grid scale oscillations. Two such schemes are the QUICK (Quadratic Upwind Interpolation for Convective Kinematics) and TOASOD (Third Order Advection Second Order Diffusion) schemes, which are similar in formulation but different in accuracy, with the two schemes being second and third order accurate in space respectively for finite difference models. These two schemes can be written in various finite difference forms for transient solute transport models, with the different representations having different numerical properties and computational efficiencies. Although these two schemes are advectively (or convectively) stable, it has been shown that the originally proposed explicit QUICK and TOASOD schemes become numerically unstable for the case of pure advection. The stability constraints have been established for each scheme representation based upon the von Neumann stability analysis. All the derived schemes have been tested for various initial solute distributions and for a number of continuous discharge cases, with both constant and time varying velocity fields. The 1-D QUICKEST (QUICK with Estimated Streaming Term) scheme is third order accurate both in time and space. It has been shown analytically and numerically that a previously derived quasi 2-D explicit QUICKEST scheme, with a reduced accuracy in time, is unstable for the case of pure advection. The modified 2-D explicit QUICKEST, ADI-TOASOD and ADI-QUICK schemes have been developed herein and proved to be numerically stable, with the bility sta- region of each derived 2-D scheme having also been established. All these derived 2-D schemesh ave been tested in a 2-D domain for various initial solute distributions with both uniform and rotational flow fields. They were further tested for a number of 2-D continuous discharge cases, with the corresponding exact solutions having also been derived herein. All the numerical tests in both the 1-D and 2-D cases were compared with the corresponding exact solutions and the results obtained using various other difference schemes, with the higher order schemes generally producing more accurate predictions, except for the characteristic based schemes which failed to conserve mass for the 2-D rotational flow tests. The ADI-TOASOD scheme has also been applied to two water quality studies in the U. K., simulating nitrate and faecal coliform distributions respectively, with the results showing a marked improvement in comparison with the results obtained by the second order central difference scheme. Details are also given of a refined numerical representation of flooding and drying of tidal flood plains for hydrodynamic modelling, with the results showing considerable improvements in comparison with a number of existing models and in good agreement with the field measured data in a natural harbour study.

Continuous casting represents 96% of all steel products made worldwide. To cast new alloys, optimal process parameters must be determined that reduce quality issues. Traditionally, this is a time-consuming and expensive process due to the need to run multiple casting trials. Alternatively, numerical models can be used to help guide development of optimal process parameters. In this thesis, a 3D thermal-solute-mechanical finite element model has been created using the THERCAST software to simulate the casting process of a new advanced high strength steel grade at Stelco’s Lake Erie Works facility. The model represents the caster from mould to exit, and takes into account heat transfer from the mould, sprays, rolls, and ambient air. The model has been extensively validated using plant measurements from steel shim trials and pyrometer data. The model is used to investigate the evolution of temperature and shell thickness along the cast length, and the effect of spray cooling and casting speed on the surface temperature at unbending to predict transverse cracking during secondary cooling. It was found that the susceptibility to cracking increased with lower casting speed and increased water spray cooling. Increasing the casting speed had a negligible effect, and it was found to decrease with decreasing water spray cooling. This decreased water spray cooling is also accompanied by an increase in metallurgical length, so further work is required to determine appropriate safety factors to ensure the steel is completely solidified. However, preliminary results of solute and mechanical models are also presented. Further work is required to improve the predictions made by these simulations. / Thesis / Master of Applied Science (MASc)

The data-driven models used for the design of powertrain controllers are typically based on the data obtained from steady-state experiments. However, they are only valid under stable conditions and do not provide any information on the dynamic behaviour of the system. In order to capture this behaviour, dynamic modelling techniques are intensively studied to generate alternative solutions for engine mapping and calibration problem, aiming to address the need to increase productivity (reduce development time) and to develop better models for the actual behaviour of the engine under real-world conditions. In this thesis, a dynamic modelling approach is presented undertaken for the prediction of NOx emissions for a 2.0 litre Diesel engine, based on a coupled pre-validated virtual Diesel engine model (GT- Suite ® 1-D air path model) and in-cylinder combustion model (CMCL ® Stochastic Reactor Model Engine Suite). In the context of the considered Engine Simulation Framework, GT Suite + Stochastic Reactor Model (SRM), one fundamental problem is to establish a real time stochastic simulation capability. This problem can be addressed by replacing the slow combustion chemistry solver (SRM) with an appropriate NOx surrogate model. The approach taken in this research for the development of this surrogate model was based on a combination of design of dynamic experiments run on the virtual diesel engine model (GT- Suite), with a dynamic model fitted for the parameters required as input to the SRM, with a zonal design of experiments (DoEs), using Optimal Latin Hypercubes (OLH), run on the SRM model. A response surface model was fitted on the predicted NOx from the SRM OLH DoE data. This surrogate NOx model was then used to replace the computationally expensive SRM simulation, enabling real-time simulations of transient drive cycles to be executed. The performance of the approach was validated on a simulated NEDC drive cycle, against experimental data collected for the engine case study. The capability of methodology to capture the transient trends of the system shows promising results and will be used for the development of global surrogate prediction models for engine-out emissions.

South Africa mines coal to supply in the growing energy demands of the country. A majority of these mines are opencast resulting in back filled pits and above ground disposal facilities. Leachate emanating from these disposal sites are saline and in most cases highly acidic. Currently the standard testing procedure to quantify expected leachate qualities include Acid Base Accounting (ABA), Net-acid Generating test (NAG), static-and kinetic leaching. The aim of this study is to model standard humidity cell leach tests performed using the PHREEQC code. This model can then be scaled up to field conditions to model 1D reactive transport. It is commonly accepted that the rate of pyrite oxidation in backfilled pits and waste storage facilities is governed by the rate of oxygen ingress and that no pyrite oxidation take place in the saturated zone. This is not the case for humidity cells, as sufficient oxygen is available for reaction. Pyrite reactions rates in humidity cells is expected to be governed by a combination of available reaction surface and ash layer resistance. This is modelled in PHREEQC (Parkhurst & Appelo, 2003) using the KINETIC block. Leachate composition is then modelled in the column by making use of the TRANSPORT block. The experimental data is fitted by using the reactive surface and ash layer diffusion coefficient as a fitting parameter. PHREEQC does not have a gas transport module to model oxygen diffusion through the column. Due to this shortfall of PHREEQC, the influence of oxygen ingress in the system can not be directly modelled under kinetic conditions. Davis and Ritchie (1986a) proposed an anlylitical solution in which the integrated sulphate production rate can be calculated for a waste heap dump. This rate takes into account the influence of oxygen ingress and the development of an ash layer resistance to the pyrite oxydation rate. This intergrated rate can then be defined in a RATES block in PHREEQC. The Aproximate Analytical Solution (AAS) model proposed by Davis and Ritchie (1986a) is used to scale up the model used for the humidity leach cell experiment. It was found from the modelling results and comparison with PYROX that the model under predicts the integrated sulphate production rate in the initial stages of the reacting waste heap dump. It does however show results that are in close agreement with the results obtained from PYROX in later stages of the lifespan of the waste heap dump. This highlight limitations to the AAS model’s applicability on geochemical problems. The model can only be applied to describe waste heap dumps where the particles at the top of the heap are fully oxidized. / MSc (Environmental Sciences), North-West University, Potchefstroom Campus, 2015

South Africa mines coal to supply in the growing energy demands of the country. A majority of these mines are opencast resulting in back filled pits and above ground disposal facilities. Leachate emanating from these disposal sites are saline and in most cases highly acidic. Currently the standard testing procedure to quantify expected leachate qualities include Acid Base Accounting (ABA), Net-acid Generating test (NAG), static-and kinetic leaching. The aim of this study is to model standard humidity cell leach tests performed using the PHREEQC code. This model can then be scaled up to field conditions to model 1D reactive transport. It is commonly accepted that the rate of pyrite oxidation in backfilled pits and waste storage facilities is governed by the rate of oxygen ingress and that no pyrite oxidation take place in the saturated zone. This is not the case for humidity cells, as sufficient oxygen is available for reaction. Pyrite reactions rates in humidity cells is expected to be governed by a combination of available reaction surface and ash layer resistance. This is modelled in PHREEQC (Parkhurst & Appelo, 2003) using the KINETIC block. Leachate composition is then modelled in the column by making use of the TRANSPORT block. The experimental data is fitted by using the reactive surface and ash layer diffusion coefficient as a fitting parameter. PHREEQC does not have a gas transport module to model oxygen diffusion through the column. Due to this shortfall of PHREEQC, the influence of oxygen ingress in the system can not be directly modelled under kinetic conditions. Davis and Ritchie (1986a) proposed an anlylitical solution in which the integrated sulphate production rate can be calculated for a waste heap dump. This rate takes into account the influence of oxygen ingress and the development of an ash layer resistance to the pyrite oxydation rate. This intergrated rate can then be defined in a RATES block in PHREEQC. The Aproximate Analytical Solution (AAS) model proposed by Davis and Ritchie (1986a) is used to scale up the model used for the humidity leach cell experiment. It was found from the modelling results and comparison with PYROX that the model under predicts the integrated sulphate production rate in the initial stages of the reacting waste heap dump. It does however show results that are in close agreement with the results obtained from PYROX in later stages of the lifespan of the waste heap dump. This highlight limitations to the AAS model’s applicability on geochemical problems. The model can only be applied to describe waste heap dumps where the particles at the top of the heap are fully oxidized. / MSc (Environmental Sciences), North-West University, Potchefstroom Campus, 2015