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by Yuen Wong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1990. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Basic Results --- p.5 / Chapter §2.1 --- General Results --- p.5 / Chapter §2.2 --- Williamson's Method --- p.8 / Chapter Chapter 3 --- Algorithms And Subroutines --- p.15 / Chapter §3.1 --- Introduction --- p.15 / Chapter §3.2 --- Increasing Determinant Method --- p.15 / Chapter §3.3 --- Williamson's Method - Direct Computation --- p.21 / Chapter §3.4 --- Williamson's Method - Increasing Determinant --- p.26 / Chapter Chapter 4 --- Comparisons And Recommendations On Algorithms --- p.32 / Chapter §4.1 --- Introduction --- p.32 / Chapter §4.2 --- Comparisons And Recommendations On IMPROV(N) --- p.32 / Chapter §4.3 --- Comparisons And Recommendations On GENHA(N) --- p.34 / Chapter §4.4 --- Comparisons And Recommendations On VTID(N) --- p.35 / Chapter §4.5 --- Summary --- p.37 / Chapter Chapter 5 --- Applications Of Hadamard Matrices --- p.38 / Chapter §5.1 --- Hadamard Matrices And Balanced Incomplete Block Designs' --- p.38 / Chapter §5.2 --- Hadamard Matrices And Optimal Weighing Designs --- p.43 / Chapter Chapter 6 --- Conclusion --- p.51 / References --- p.52 / Appendices --- p.53

The three-dimensional lid-driven cavity flow is investigated at Reynolds Number(Re)=10,000 for a wide range of spanwise-aspect ratios of 3:1:1, 0.5:1:1, and 1:1:1 using the Partially Averaged Navier-Stokes(PANS) turbulence closure model. The PANS turbulence model is a variable resolution turbulence closure model, where the unresolved-to-total ratios of kinetic energy (fk) and dissipation (fe), serve as resolution control parameters. This study focuses on two main aspects of PANS: (i) the evaluation of Turbulent transport models and (ii) the effect of grid spacing on accuracy of the numerical solution. PANS calculations are tested against LES and experimental results of Jordan (1994), in terms of both qualitative and quantitative quantities. The main coclusions are are: (i) for a given fk value, the Zero-Transport model is superior to the Maximum-Transport model for unresolved dissipation, (ii) both models are adequate for unresolved kinetic energy, and (iii) for a given grid size, the results depend heavily on grid spacing especially for larger fk values.

The three-dimensional lid-driven cavity flow is investigated at Reynolds Number(Re)=10,000 for a wide range of spanwise-aspect ratios of 3:1:1, 0.5:1:1, and 1:1:1 using the Partially Averaged Navier-Stokes(PANS) turbulence closure model. The PANS turbulence model is a variable resolution turbulence closure model, where the unresolved-to-total ratios of kinetic energy (fk) and dissipation (fe), serve as resolution control parameters. This study focuses on two main aspects of PANS: (i) the evaluation of Turbulent transport models and (ii) the effect of grid spacing on accuracy of the numerical solution. PANS calculations are tested against LES and experimental results of Jordan (1994), in terms of both qualitative and quantitative quantities. The main coclusions are are: (i) for a given fk value, the Zero-Transport model is superior to the Maximum-Transport model for unresolved dissipation, (ii) both models are adequate for unresolved kinetic energy, and (iii) for a given grid size, the results depend heavily on grid spacing especially for larger fk values.

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