This book introduces a new generation of superfast algorithmsfor the treatment of the notoriously difficult velocity-pressure couplingproblem in incompressible fluid flow solutions. It provides all the necessary details for the understanding andimplementation of the procedures. The derivation and construction of thefully-implicit, block-coupled, incomplete decomposition mechanism are given ina systematic, but easy fashion. Worked-out solutions are included, withcomparisons and discussions. A complete program code is included for fasterimplementation of the algorithm. A brief literature review…mehr
This book introduces a new generation of superfast algorithmsfor the treatment of the notoriously difficult velocity-pressure couplingproblem in incompressible fluid flow solutions. It provides all the necessary details for the understanding andimplementation of the procedures. The derivation and construction of thefully-implicit, block-coupled, incomplete decomposition mechanism are given ina systematic, but easy fashion. Worked-out solutions are included, withcomparisons and discussions. A complete program code is included for fasterimplementation of the algorithm. A brief literature review of the developmentof the classical solution procedures is included as well.
Preface.- Chapter1 Introduction.- 1.1 Scope of the Book.- 1.2 Outline of the Book.- Chapter 2Preliminaries.- 2.1 Quadratic Interpolation.- 2.2 Approximations usingLagrangian Polynomial.- 2.3 Approximations using Taylor Series.- 2.4 GeneralElimination Technique for Linear Systems.- 2.5 Solution Techniques for SpecialLinear Systems.- Chapter 3 Governing Differential Equations.- 3.1 GoverningEquations.- 3.2 Characteristics of the Governing Equations.- 3.3 TheVelocity-Pressure Coupling Problem.- Chapter 4 Finite Difference Formulations.-4.1 Manipulation of the Momentum Equations.- 4.2 Grid Arrangement for theSolution .- 4.3 Profile Assumptions for the Discretizations.- 4.4Discretization of the Governing Equations.- 4.5 A Discussion on the ProfileAssumptions.- Chapter 5 Preparations For Solution.- 5.1 The Solution Region.- 5.2 Boundary Conditions.- 5.3 Incorporating Relaxation.- Chapter 6 Assembling The Discretized EquationsInto A Block Matrix System.- 6.1 The Numbering Scheme.- 6.2 Construction of theBlock Matrix System.- 6.3. Disadvantagesof the Block Matrix.- Chapter 7 The Solution Procedure: Block IncompleteDecomposition.- 7.1 Properties and Advantages of the Block Matrix.- 7.2 GeneralIncomplete 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 ImplicitCoupled Solution- SICS).- Chapter 8 Applications And Testing.- 8.1Benchmark Fluid Flow Problems.- 8.2 Testing Criteria.- 8.3 Performance Analysisand Comparisons.- 8.4 A Discussion of the Mechanism of the Procedures.- 8.5Comparison with the Segregated-Type Procedures.- 8.6 ConvergenceCharacteristics and Performances of SICS and SIMPLER: A Relative Comparison.- Chapter9: Special Cases.- 9.1 Time-Dependent Problems.- 9.2 Stoke's Flow Equations.- 9.3Turbulent Flows and Heat Transfer.- 9.4Adaptation to Existing Codes.- 9.5 Three-Dimensional Problems.- Chapter 10 Concluding Remarks.- Appendix A: A Critical Survey ofLiterature-an Adventure Into Perfection.- Appendix B: Segregated SolutionProcedures: Simple And Simpler.- Appendix C: Fortran Subroutines -Blocksolfics2 and Blocksolsics.- References.- Nomenclature.- Index.
Preface.- Chapter1 Introduction.- 1.1 Scope of the Book.- 1.2 Outline of the Book.- Chapter 2Preliminaries.- 2.1 Quadratic Interpolation.- 2.2 Approximations usingLagrangian Polynomial.- 2.3 Approximations using Taylor Series.- 2.4 GeneralElimination Technique for Linear Systems.- 2.5 Solution Techniques for SpecialLinear Systems.- Chapter 3 Governing Differential Equations.- 3.1 GoverningEquations.- 3.2 Characteristics of the Governing Equations.- 3.3 TheVelocity-Pressure Coupling Problem.- Chapter 4 Finite Difference Formulations.-4.1 Manipulation of the Momentum Equations.- 4.2 Grid Arrangement for theSolution .- 4.3 Profile Assumptions for the Discretizations.- 4.4Discretization of the Governing Equations.- 4.5 A Discussion on the ProfileAssumptions.- Chapter 5 Preparations For Solution.- 5.1 The Solution Region.- 5.2 Boundary Conditions.- 5.3 Incorporating Relaxation.- Chapter 6 Assembling The Discretized EquationsInto A Block Matrix System.- 6.1 The Numbering Scheme.- 6.2 Construction of theBlock Matrix System.- 6.3. Disadvantagesof the Block Matrix.- Chapter 7 The Solution Procedure: Block IncompleteDecomposition.- 7.1 Properties and Advantages of the Block Matrix.- 7.2 GeneralIncomplete 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 ImplicitCoupled Solution- SICS).- Chapter 8 Applications And Testing.- 8.1Benchmark Fluid Flow Problems.- 8.2 Testing Criteria.- 8.3 Performance Analysisand Comparisons.- 8.4 A Discussion of the Mechanism of the Procedures.- 8.5Comparison with the Segregated-Type Procedures.- 8.6 ConvergenceCharacteristics and Performances of SICS and SIMPLER: A Relative Comparison.- Chapter9: Special Cases.- 9.1 Time-Dependent Problems.- 9.2 Stoke's Flow Equations.- 9.3Turbulent Flows and Heat Transfer.- 9.4Adaptation to Existing Codes.- 9.5 Three-Dimensional Problems.- Chapter 10 Concluding Remarks.- Appendix A: A Critical Survey ofLiterature-an Adventure Into Perfection.- Appendix B: Segregated SolutionProcedures: Simple And Simpler.- Appendix C: Fortran Subroutines -Blocksolfics2 and Blocksolsics.- References.- Nomenclature.- Index.
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