PHYSICAL FLUID DYNAMICS
1 Introduction 1 11 Scope of the Book 1 12 Outline of the Book 4 2 Preliminaries 7 21 Quadratic Interpolation 7 22 Approximations Using Lagrangian Polynomial 8 23 Approximations Using Taylor Series 10 24 General Elimination Technique for Linear Systems 13 25 Solution Techniques for Special Linear Systems 16 3 Governing Differential Equations 19 31 Governing Equations 19 32 Characteristics of the Governing Equations 20 33 The Velocity-Pressure Coupling Problem 21 4 Finite Difference Formulations 25 41 Manipulation of the Momentum Equations 25 42 Grid Arrangement for the Solution 26 43 Profile Assumptions for the Discretizations 28 44 Discretization of the Governing Equations 31 441 Discretization of the u-Momentum Equation 31 442 Discretization of the v-Momentum Equation 35 443 Discretization of the Mass Conservation Equation 38 45 A Discussion on the Profile Assumptions 38 5 Preparations for Solution 41 51 The Solution Region 41 52 Boundary Conditions 42 521 Types of Boundary Conditions 43 522 Application of Various Types of Boundary Conditions into the Momentum Equations 45 523 Application of Boundary Conditions into the Coupled Equations 47 53 Incorporating Relaxation 54 6 Assembling the Discretized Equations into a Block Matrix System 57 61 The Numbering Scheme 57 62 Construction of the Block Matrix System 58 63 Disadvantages of the Block Matrix 61 7 The Solution Procedure: Block Incomplete Decomposition 65 71 Properties and Advantages of the Block Matrix 66 72 General Incomplete Decomposition 68 73 An Incomplete Decomposition of the Block System (BIP) 71 74 The Block Solution Procedure 77 75 Complete Solution of the Flow Field 78 76 A Family of Procedures: BIPEN, FICS-1, FICS-2 78 77 Storage Requirements and Complexity 82 771 Storage Requirements 82 772 Complexity 83 78 The Simplest Case (Simple Implicit Coupled Solution—SICS) 84 781 The Solution Algorithm (SICS) 85 782 Properties and Benefits of SICS 87 8 Applications and Testing 89 81 Benchmark Fluid Flow Problems 89 82 Testing Criteria 99 83 Performance Analysis and Comparisons 102 84 A Discussion of the Mechanism of the Procedures 106 85 Comparison with the Segregated-Type Procedures 108 86 Convergence Characteristics and Performances of SICS and SIMPLER: A Relative Comparison 109 9 Special Cases 115 91 Time-Dependent Problems 115 92 Stoke’s Flow Equations 119 93 Turbulent Flows and Heat Transfer 119 94 Adaptation to Existing Codes 120 95 Three-Dimensional Problems 120 10 Concluding Remarks 127 References 127