Solute transport studies frequently rely on numerical solutions of the classical advection-diffusion equation. Unfortunately, solutions obtained with traditional finite difference and finite element techniques typically exhibit excessive numerical diffusion or spurious oscillation when advection dominates, especially when velocity field is highly variable. One recently developed technique, the finite analytic method, offers an attractive alternative. Finite analytic methods utilize local analytic solutions in discrete elements to obtain the algebraic representations of the governing partial differential equations, thus eliminating the truncation error in the finite difference and the use of approximating functions in the finite element method. The finite analytic solutions have been shown to be stable and numerically robust for advection-dominated transport in heterogeneous velocity fields. However, the existing finite analytic methods for solute transport in multiple dimensions have the following disadvantages. First, the method is computationally inefficient when applied to heterogeneous media due to the complexity of the formulation. Second, the evaluation of finite analytic coefficients is when the Peclet number is large. Third, the method introduces significant numerical diffusion due to inadequate temporal approximation when applied to transient problems. This thesis develops improved finite analytic methods for two-dimensional steady as well as unsteady solute transports in steady velocity fields. For steady transport, the new method exploits the advantages of the existing finite analytic and finite difference methods. The analytically difficult diffusion terms are approximated by finite difference and numerically difficult advection and reaction terms are treated analytically in a local element in deriving the numerical schemes. The new finite analytic method is extended to unsteady transport through application of Laplace transformation. Laplace transformation converts the transient equation to a steady-state expression that can be solved with the steady version of the improved finite analytic method. Numerical inversion of the transformed variables is used to recover solute concentration in the physical space-time domain. The effectiveness and accuracy of the new finite analytic method is demonstrated through stringent test examples of two dimensional steady-state transport in highly variable velocity fields. The results clearly demonstrated that the improved finite analytic methods are efficient, robust and accurate.

Background. Extensive studies have been conducted to simulate blood flow in the human vasculature using nonlinear equations of pulsatile flow in collapsible tube plus a network of vessels to represent the whole vasculature and the cerebral circulation. For non-linear models numerical solutions are obtained for the fluid flow equations. Methods. Equations of fluid motion in collapsible tubes were developed in the presence of gravitational force (Gforce). The Lax-Wendroff and MacCormack methods were used to solve the governing equations and compared both in terms of accuracy, convergence, and computer processing (CPU) time. A modified vasculature of the whole body and the cerebral circulation was developed to obtain a realistic simulation of blood flow under different conditions. The whole body vasculature was used to validate the simulation in terms of input impedance and wave transmission. The cerebral vasculature was used to simulate conditions such as presence of G-force, blockage of Internal Carotid Artery (ICA), and the effects on cerebral blood flow of changes in mean and pulse pressure. Results. The simulation results for zero G-force were in very good agreement with published experimental data as was the simulation of cerebral blood flow. Both numerical methods for solutions of governing equations gave similar results for blood flow simulations but differed in calculation performance and stability depending on levels of G-force. Simulation results for uniform and sinusoidal G-force are also in good agreement with published experimental results, Blood flow was simulated in the presence of a single (left) carotid artery obstruction with varying morphological structures of the Circle of Willis (CoW). This simulation showed significant differences in contralateral blood flow in the presence or absence of communicating arteries in the CoW. It also was able to simulate the decreases in blood flow in the cerebral circulation compartment corresponding to the visual cortex in the presence of G-force. This is consistent with the known loss of vision under increased acceleration. Conclusions. This study has shown that under conditions of gravitational forces physiological changes in blood flow in the systemic and cerebral vasculature can be simulated realistically by solving the one-dimentional fluid flow equations and non-linear vascular properties numerically. The simulation was able to predict changes in blood flow with different configurations and properties of the vascular network.

Bibliography: leaves 184-190 / viii, 190 leaves : ill ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Applied Mathematics, 1987

A literature review of current phase separation publications was conducted. Data sets were collected and compiled into a Two-Phase Flow Separation Database. Examination of this database indicating a need for further investigation into the liquid entertainment phenomena for smaller hot-leg to branch diameters and intermittent flow regimes. A detailed analysis to the prototypic phase separation process is presented and the associated phenomena are identified. Appropriate scaling criteria were employed for the design of a scaled test facility. Geometry and the flow conditions of the test facility were determined accordingly to Wu et. al (1998). A series of phase separation tests conducted at the Air-water Test Loop for Advanced Thermal-hydraulic Studies (ATLATS) and Advanced Plan Experiment (APEX) has been completed. Results show that the criteria developed by Smoglie (1984) used in RELAP5, reasonably predicts the onset of liquid entrainment. However, the steady-state entrainment correlation in RELAP5 significantly underpredicts primary coolant removal rates. This discrepancy is due to the effects of downstream boundary conditions and pool entrainment and carry-over from the reactor vessel. Due to pool entrainment, entrainment through the branch continues when the reactor vessel mixture level drops below the bottom of the hot-leg. This investigation shows that RELAP5 is non-conservative when predicting coolant removal rates due to steady state liquid entrainment in a horizontal mainline with a vertical branch for stratified, stratified-wavy, transition, and stepped hot-leg flow regimes. / Graduation date: 2001

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