# 臺灣博碩士論文加值系統

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 CoverContents1. Introduction1.1 Finite Element Method and Imcompressibility Constraint1.2 Upwind Schemes1.3 Stationary and Non-stationary Approaches1.4 Non-primitive Variable Formulations1.5 Primitive Varibale Formulations1.6 Solution of Nonlinear Problem1.7 Solvers of Linear Equations1.8 Outflow Boundary Condition (OBC)1.9 Aims of This Study2. Mathematial Fundamentals2.1 Stationary Primitive Variable Formulation2.2 Weak Formulation2.3 Numerical Integration2.4 Nonlinear Iterative Solver3. Streamiline Upwind for Quadratic Elements3.1 Upwind Finite Element Model3.1.1 Explicit artificial viscosity finite element model3.1.2 Streamline Upwind Petrov-Galerkin (SUPG) finite element model3.2 Fundamental Studies on the Discretizatin Scheme3.2.1 Modified equation for continuity and momentum equations3.3 Computed Results3.3.1 Test problem 13.3.2 Test problem 23.3.3 Test problem 33.4 Conclusions4. Monotonic pETROV-gALERKIN Formulation4.1 Multi-dimensional Flux Discretization Scheme4.1.1 Model equation and discretization method4.1.2 Construction of test space4.1.3 Accuracy4.1.4 Monotonicity4.2 Refinement on Monotonicity-preservation Upwind Model4.3 Extension to Stationary Incompressible Navier-Stokes Flow4.4 Computed Results4.4.1 Problem without a boundary layer4.4.2 Problem with a boundary layer4.4.3 Skew convection-diffusion problem4.4.4 Convection-diffusion problem of Smith and Hutton4.4.5 Analytic study on stationary Navier-Stokes equations4.4.6 Lid-driving cavity flow Problem4.5 Conclusions5. Legendre Ploynomial Space5.1 Test Functions Spanned by Legendre Polynomials5.2 Computed Results5.3 Conclusions6. Free Boundary Condition6.1 Boundary Condition6.1.1 General remarks and literature review6.1.2 Free boundary codition6.2 Computed Results6.2.1 Analytic validation6.2.2 Backward-facing step internal flow problem6.2.3 Flow analysis in a wharf6.3 Conclusions7. Comparison on Three-dimensional Elements7.1 Bsis Functions for Primitive Variables7.1.1 Continuous pressure elements7.1.2 Discontinuous pressure elements7.1.3 R2+-P0 element (or 26/1 elements)7.2 Constraint Counts on the Investigated Elements7.3 Solution Solver7.4 Computed Results7.5 Conclusions8. Bi-CGSTAB Iterative Method for Three Dimensional Problems8.1 Discrete Divergence-free Velocities8.2 Element-By-Element Iterative Solver8.2.1 Iterative methods for dealing with asymmetry8.2.2 Element-by-element Bi-CGSTAB method8.3 Computed Results8.3.1 Analytic Navier -Stokes equations in three dimensions8.3.2 Lid-driven cubical cavity flow problem8.3.3 Parallelism study8.4 Conclusions9. Compact Elements on Three-dimensional Problems9.1 Multi-Variant Basis Space9.1.1 Q1+-P0 element(or 14/1 element)9.1.2 Constraint Q1+-P0 element(or 14/1c element)9.2 Compressed row Storage(CRS)Data sTRUCTURE9.3 Unsymmetric Multi-Frontal LU Solution Solver9.4 Computed Results9.5 Conclusions10. Concluding RemarksA Functional SpaceB Derivations of Upwinding CoefficientsB1. Derivations of δEB2. Derivations of δCC Bridf Manual of PFEM2D Version 1.0Others
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