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研究生:王明達
論文名稱:發展求解不可壓縮黏性流之有限元素方法
論文名稱(外文):Development of finite element method for incompressible navier-stokes equations
指導教授:許文翰
學位類別:博士
校院名稱:國立臺灣大學
系所名稱:造船及海洋工程學研究
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:1996
畢業學年度:85
語文別:中文
相關次數:
  • 被引用被引用:2
  • 點閱點閱:120
  • 評分評分:
  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:0
Cover
Contents
1. Introduction
1.1 Finite Element Method and Imcompressibility Constraint
1.2 Upwind Schemes
1.3 Stationary and Non-stationary Approaches
1.4 Non-primitive Variable Formulations
1.5 Primitive Varibale Formulations
1.6 Solution of Nonlinear Problem
1.7 Solvers of Linear Equations
1.8 Outflow Boundary Condition (OBC)
1.9 Aims of This Study
2. Mathematial Fundamentals
2.1 Stationary Primitive Variable Formulation
2.2 Weak Formulation
2.3 Numerical Integration
2.4 Nonlinear Iterative Solver
3. Streamiline Upwind for Quadratic Elements
3.1 Upwind Finite Element Model
3.1.1 Explicit artificial viscosity finite element model
3.1.2 Streamline Upwind Petrov-Galerkin (SUPG) finite element model
3.2 Fundamental Studies on the Discretizatin Scheme
3.2.1 Modified equation for continuity and momentum equations
3.3 Computed Results
3.3.1 Test problem 1
3.3.2 Test problem 2
3.3.3 Test problem 3
3.4 Conclusions
4. Monotonic pETROV-gALERKIN Formulation
4.1 Multi-dimensional Flux Discretization Scheme
4.1.1 Model equation and discretization method
4.1.2 Construction of test space
4.1.3 Accuracy
4.1.4 Monotonicity
4.2 Refinement on Monotonicity-preservation Upwind Model
4.3 Extension to Stationary Incompressible Navier-Stokes Flow
4.4 Computed Results
4.4.1 Problem without a boundary layer
4.4.2 Problem with a boundary layer
4.4.3 Skew convection-diffusion problem
4.4.4 Convection-diffusion problem of Smith and Hutton
4.4.5 Analytic study on stationary Navier-Stokes equations
4.4.6 Lid-driving cavity flow Problem
4.5 Conclusions
5. Legendre Ploynomial Space
5.1 Test Functions Spanned by Legendre Polynomials
5.2 Computed Results
5.3 Conclusions
6. Free Boundary Condition
6.1 Boundary Condition
6.1.1 General remarks and literature review
6.1.2 Free boundary codition
6.2 Computed Results
6.2.1 Analytic validation
6.2.2 Backward-facing step internal flow problem
6.2.3 Flow analysis in a wharf
6.3 Conclusions
7. Comparison on Three-dimensional Elements
7.1 Bsis Functions for Primitive Variables
7.1.1 Continuous pressure elements
7.1.2 Discontinuous pressure elements
7.1.3 R2+-P0 element (or 26/1 elements)
7.2 Constraint Counts on the Investigated Elements
7.3 Solution Solver
7.4 Computed Results
7.5 Conclusions
8. Bi-CGSTAB Iterative Method for Three Dimensional Problems
8.1 Discrete Divergence-free Velocities
8.2 Element-By-Element Iterative Solver
8.2.1 Iterative methods for dealing with asymmetry
8.2.2 Element-by-element Bi-CGSTAB method
8.3 Computed Results
8.3.1 Analytic Navier -Stokes equations in three dimensions
8.3.2 Lid-driven cubical cavity flow problem
8.3.3 Parallelism study
8.4 Conclusions
9. Compact Elements on Three-dimensional Problems
9.1 Multi-Variant Basis Space
9.1.1 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 sTRUCTURE
9.3 Unsymmetric Multi-Frontal LU Solution Solver
9.4 Computed Results
9.5 Conclusions
10. Concluding Remarks
A Functional Space
B Derivations of Upwinding Coefficients
B1. Derivations of δE
B2. Derivations of δC
C Bridf Manual of PFEM2D Version 1.0
Others
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