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.

Serves as new benchmark book for application research Contains all details of construction for implementing the procedures Includes solved problems and applications Includes supplementary material: sn.pub/extras

Inhalt

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 ( S imple I mplicit C oupled S olution- 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 Literaturean Adventure Into Perfection.- Appendix B: Segregated Solution Procedures: Simple And Simpler.- Appendix C: Fortran Subroutines Blocksolfics2 and Blocksolsics. - References.- Nomenclature.- Index. <p