Fully Implicit, Coupled Procedures in Computational Fluid Dynamics

This book introduces a new generation of superfast algorithms for the treatment of the notoriously difficult velocity-pressure coupling problem in incompressible fluid flow solutions. It provides all the necessary details for the understanding and implementation of the procedures. The derivation and construction of the fully-implicit, block-coupled, incomplete decomposition mechanism are given in a systematic, but easy fashion. Worked-out solutions are included, with comparisons and discussions. A complete program code is included for faster implementation of the algorithm. A brief literature review of the development of the classical solution procedures is included as well.

Contenu

Preface.- Chapter 1 Introduction.- 1.1 Scope of the Book.- 1.2 Outline of the Book.- Chapter 2 Preliminaries.- 2.1 Quadratic Interpolation.- 2.2 Approximations using Lagrangian Polynomial.- 2.3 Approximations using Taylor Series.- 2.4 General Elimination Technique for Linear Systems.- 2.5 Solution Techniques for Special Linear Systems.- Chapter 3 Governing Differential Equations.- 3.1 Governing Equations.- 3.2 Characteristics of the Governing Equations.- 3.3 The Velocity-Pressure Coupling Problem.- Chapter 4 Finite Difference Formulations.- 4.1 Manipulation of the Momentum Equations.- 4.2 Grid Arrangement for the Solution .- 4.3 Profile Assumptions for the Discretizations.- 4.4 Discretization of the Governing Equations.- 4.5 A Discussion on the Profile Assumptions.- Chapter 5 Preparations For Solution.- 5.1 The Solution Region.- 5.2 Boundary Conditions.- 5.3 Incorporating Relaxation.- Chapter 6 Assembling The Discretized Equations Into A Block Matrix System.- 6.1 The Numbering Scheme.- 6.2 Construction of the Block Matrix System.- 6.3. Disadvantages of the Block Matrix.- Chapter 7 The Solution Procedure: Block Incomplete Decomposition.- 7.1 Properties and Advantages of the Block Matrix.- 7.2 General Incomplete Decomposition.- 7.3 An Incomplete Decomposition of the Block System (BIP).- 7.4 The Block Solution Procedure.- 7.5 Complete Solution of the Flow Field.- 7.6 A Family of Procedures: BIPEN, FICS-1, FICS-2.- 7.7 Storage Requirements and Complexity.- 7.8 The Simplest Case (Simple Implicit Coupled Solution- SICS).- Chapter 8 Applications And Testing.- 8.1 Benchmark Fluid Flow Problems.- 8.2 Testing Criteria.- 8.3 Performance Analysis and Comparisons.- 8.4 A Discussion of the Mechanism of the Procedures.- 8.5 Comparison with the Segregated-Type Procedures.- 8.6 Convergence Characteristics and Performances of SICS and SIMPLER: A Relative Comparison.- Chapter 9: Special Cases.- 9.1 Time-Dependent Problems.- 9.2 Stoke's Flow Equations.- 9.3 Turbulent Flows and Heat Transfer.- 9.4 Adaptation to Existing Codes.- 9.5 Three-Dimensional Problems.- Chapter 10 Concluding Remarks.- Appendix A: A Critical Survey of Literature-an Adventure Into Perfection.- Appendix B: Segregated Solution Procedures: Simple And Simpler.- Appendix C: Fortran Subroutines - Blocksolfics2 and Blocksolsics.- References.- Nomenclature.- Index.