In this thesis, a parallel solver was developed for the modelling of blood flow through a number of patient-specific geometries. A locally conservative Galerkin (LCG) spatial discretisation was applied along with an artificial compressibility and characteristic based split (CBS) scheme to solve the 3D incompressible Navier-Stokes equations. The Spalart-Allmaras one equation turbulence model was also optionally employed. The solver was constructed using FORTRAN and the Message Passing Interface (MPI). Parallel testing demonstrated linear or better than linear speedup on hybrid patient-specific meshes. These meshes were unstructured with structured boundary layers. From the parallel testing it is clear that the significance of inter-processor communication is negligible in a three dimensional case. Preliminary tests on a short patient-specific carotid geometry demonstrated the need for ten or more boundary layer meshes in order to sufficiently resolve the peak wall shear stress (WSS) along with the peak time-averaged WSS. A time sensitivity study was also undertaken along with the assessment of the order of the real time step term. Three backward difference formulae (BDF) were tested and no significant difference between them was detected. Significant speedup was possible as the order of time discretisation increased however, making the choice of BDF important in producing a timely solution. Followed by the preliminary investigation, four more carotid geometries were investigated in detail. A total of six haemodynamic wall parameters have been brought together to analyse the regions of possible atherogenesis within each carotid. The investigations revealed that geometry plays an overriding influence on the wall parameter distribution. Each carotid artery displayed high time-averaged WSS at the apex, although the value increased significantly with a proximal stenosis. Two out of four meshes contained a region of low time-averaged WSS distal to the flow divider and within the largest connecting artery (internal or external carotid artery), indicating a potential region of atherosclerosis plaque formation. The remaining two meshes already had a stenosis in the corresponding region. This is in excellent agreement with other established works. From the investigations, it is apparent that a classification system of stenosis severity may be possible with potential application as a clinical diagnosis aid. Finally, the flow within a thoracic aortic aneurysm was investigated in order to assess the influence of a proximal folded neck. The folded neck had a significant effect on the wall shear stress, increasing by up to 250% over an artificially smoothed neck. High wall shear stresses may be linked to aneurysm rupture. Being proximal to the aneurysm, this indicated that local geometry should be taken into account when assessing the rupture potential of an aneurysm.

The water in most reservoirs is density stratified with depth. This stratification leads to the inhibition of vertical movement, consequently, when water is withdrawn from the reservoir it tends to move in a jet-like layer called a withdrawal layer, towards the sink. By placing the sink at a certain depth, one is able to selectively withdrawal water from a limited range of depths and thus obtain water of a desired quality. Much work has been done in this field by considering a simplified boundary geometry, usually rectangular. However little attention has been given to the effects of accurate boundary geometry. For this thesis, five numerical experiments were conducted for the problem of a two-dimensional, viscous, incompressible, slightly-stratified flow towards a sink in a triangular reservoir. / Science, Faculty of / Mathematics, Department of / Graduate

This thesis develops a model for the management of till cash (currency and coin) of a branch for a Vancouver area credit union. The model is developed in two parts. First, a model is estimated to forecast cash demand and then a cash order algorithm is developed. Two statistical models are developed to estimate cash demand. The first employs Box-Jenkins time series techniques. This model fails because the cash flow data are non-stationary, exhibiting both a growth trend and high autocorrelations at large lags. In the second model, a growth trend for real weekly cash flows is first estimated, incorporating an asymptotic capacity constraint. The real cash flow trend is converted to a nominal trend and used as the weight in a linear weighted least squares model for daily cash flows, in which the explanatory variables are dummy variables to indicate days of the week, months of the year, incidence of pay days, etc. The consistency of the resulting forecast model is also discussed. To develop a cash order algorithm, steady state models are first considered. These models are generally based on stationary cash demand, constant delivery lag times for orders and other assumptions that are inappropriate in this till cash management setting. To relax the steady state assumptions a general dynamic programming framework is developed for the cash management model that allows for either penalty costs for cash-outs (cash shortages) or a chance constraint involving the probability of a cash-out. Because of non-stationarity of the cash flows the dynamic program cannot be solved directly, but an approximate solution is obtained using a simulation technique. The resulting algorithm is tested on historical data and the results are discussed briefly. / Business, Sauder School of / Graduate

Many conceptual models have been proposed to explain the fluid-flow mechanism responsible for the origin of carbonate-hosted lead-zinc deposits such as those in the Mississippi Valley and at Pine Point. This study is devoted to the quantitative investigation of one ore-genesis mechanism: gravity-driven groundwater-flow systems. Numerical modeling techniques are used to develop a self-contained computer code for two-dimensional simulation of regional transport processes along cross sections through sedimentary basins. The finite-element method is applied to solve the steady-state, fluid-flow and heat-transport equations, and a moving-particle random-walk model is developed to predict the dispersion and advection of aqueous components. The program EQ3/EQ6 is used to compute possible reaction-path scenarios at the ore-forming site. Full integration of geochemical calculations into the transport model is currently impractical because of computer-time limitations. Results of a sensitivity analysis indicate that gravity-driven ground-water-flow systems are capable of sustaining favorable fluid-flow rates, temperatures, and metal concentrations, for ore formation near the thin edge of a basin. Dispersive processes render long-distance transport of metal and sulfide in the same fluid an unlikely process in the genesis of large ore deposits, unless metal and sulfide are being added to the fluid along the flow path. The transport of metal in sulfate-type brines is a more defensible model, in which case the presence of reducing agents control the location of ore deposition. Hydrodynamic conditions that could result.--in ore formation through mixing of two fluids are rare. The theoretical approach is a powerful tool for gaining insight into the role of fluid flow in ore genesis and in the study of specific ore districts. A preliminary model of the Pine Point deposit suggests paleoflow rates on the order of 1.0 to 5.0 m³/m² yr, paleoconcentrations of zinc on the order of 1.0 to 5.0 mg/kg • H₂O, and paleotemperatures in the range 60°C to 100°C. Under these conditions, the time required for the formation of Pine Point would be on the order of 0.5 to 5.0 million years. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate

The development of connected and automated vehicle (CAV) technologies motivate modeling efforts and studies to understand CAVs' collective behaviors on public roads. In this thesis, we study CAV traffic flows through macroscopic models under two mathematical frameworks: the nonlocal conservation laws and the mean field games.The nonlocal conservation law models incorporate traffic information in a nonlocal range into each vehicle's driving control. We study one such model with a finite spatial nonlocal range, and demonstrate that proper use of the nonlocal information will offer better traffic stability. We also discuss numerical computation of the model that is robust under the changes of the nonlocal range. The mean field game models consider strategic interactions between CAVs, assuming each vehicle anticipates future traffic conditions and plans its driving control to minimize a predefined driving cost. A systematic approach is developed to derive the model, solve the model, and test the equilibrium solution. We take this approach in several traffic scenarios for CAVs on a single road or on a network, and demonstrate that proper design of the CAV driving cost function can lead to more efficient and stable traffic flows than human traffics. The established results in the thesis will bring more mathematical understandings on the proposed and studied models. The results may also provide insights on how to utilize the vehicle connectivity and automation to improve the overall traffic, and help to the CAV driving algorithm design.

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