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Computational Fluid Dynamics Based on the Unified Coordinates

Computational Fluid Dynamics Based on the Unified Coordinates
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10022725 Access this eBook online Ebook for Engineering   GUtech Library . . Available .  
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ISBN 9783642258961
9783642258954
Author Hui, Wai-How
Title Computational Fluid Dynamics Based on the Unified Coordinates
1st ed.
Description 1 online resource (189 pages)
Contents Title Page -- Copyright Page -- Preface -- Table of Contents -- Chapter 1 Introduction -- 1.1 CFD as Numerical Solution to Nonlinear Hyperbolic PDEs -- 1.2 Role of Coordinates in CFD -- 1.2.1 Theoretical Issues -- 1.2.2 Computational Issues -- 1.3 Outline of the Book -- References -- Chapter 2 Derivation of Conservation Law Equations -- 2.1 Fluid as a Continuum -- 2.2 Derivation of Conservation Law Equations in Fixed Coordinates -- 2.3 Conservation Law Equations in Moving Coordinates -- 2.4 Integral Equations versus Partial Differential Equations -- 2.5 The Entropy Condition for Inviscid Flow Computation -- References -- Chapter 3 Review of Eulerian Computation for 1-D Inviscid Flow -- 3.1 Flow Discontinuities and Rankine-Hugoniot Conditions -- 3.1.1 Special Case: Stationary Surface of Discontinuity -- 3.1.2 General Case: Moving Surface of Discontinuity -- 3.2 Classification of Flow Discontinuities -- 3.2.1 Special Case: Stationary Surface of Discontinuity -- 3.2.2 General Case: Moving Surface of Discontinuity -- 3.3 Riemann Problem and its Solution -- 3.3.1 Elementary Waves -- 3.3.2 Existence and Uniqueness of Solution -- 3.3.3 Structure of Riemann Solution for 1-D Flow -- 3.3.4 Solution of the Elementary Waves -- 3.3.5 Solution Algorithm -- 3.4 Preliminary Considerations of Numerical Computation -- 3.4.1 The Question of Weak Solution to Partial Differential Equations -- 3.4.2 Finite Volume Formulation -- 3.5 Godunov Scheme -- 3.6 High Resolution Schemes and Limiters -- 3.7 Defects of Eulerian Computation -- References -- Chapter 4 1-D Flow Computation Using the Unified Coordinates -- 4.1 Gas Dynamics Equations Based on the Unified Coordinates -- 4.2 Shock-Adaptive Godunov Scheme -- 4.3 The Use of Entropy Conservation Law for Smooth Flow Computation -- 4.4 The Unified Computer Code.
4.5 Cure of Defects of Eulerian and Lagrangian Computation by the UC Method -- 4.5.1 Contact smearing -- 4.5.2 Slow moving shock -- 4.5.3 Sonic point glitch -- 4.5.4 Start-up errors[12] -- 4.5.5 Low pressure flow -- 4.5.6 Wall-overheating -- 4.5.7 Strong rarefaction waves -- 4.6 Conclusions -- References -- Chapter 5 Comments on Current Methods for Multi-Dimensional Flow Computation -- 5.1 Eulerian Computation -- 5.2 Lagrangian Computation -- 5.3 The ALE Computation -- 5.4 Moving Mesh Methods -- 5.5 Optimal Coordinates -- References -- Chapter 6 The Unified Coordinates Formulation of CFD -- 6.1 Hui Transformation -- 6.2 Geometric Conservation Laws -- 6.3 Derivation of Governing Equations in Conservation Form -- References -- Chapter 7 Properties of the Unified Coordinates -- 7.1 Relation to Eulerian Computation -- 7.2 Relation to Classical Lagrangian Coordinates -- 7.3 Relation to Arbitrary-Lagrangian-Eulerian Computation -- 7.4 Contact Resolution -- 7.5 Mesh Orthogonality -- 7.6 Unified Coordinates for Steady Flow -- 7.7 Effects of Mesh Movement on the Flow -- 7.8 Relation to Other Moving Mesh Methods -- 7.9 Relation to Mesh Generation and the Level-Set Function Method -- References -- Chapter 8 Lagrangian Gas Dynamics -- 8.1 Lagrangian Gas Dynamics Equations -- 8.2 Weak Hyperbolicity -- 8.3 Non-Equivalency of Lagrangian and Eularian Formulation -- References -- Chapter 9 Steady 2-D and 3-D Supersonic Flow -- 9.1 The Unified Coordinates for Steady Flow -- 9.2 Euler Equations in the Unified Coordinates -- 9.3 The Space-Marching Computation -- 9.4 Examples -- 9.5 3-D Flow -- References -- Chapter 10 Unsteady 2-D and 3-D Flow Computation -- 10.1 Summary of Solution to the 2-D Euler Equations Using the Unified Coordinates -- 10.2 Computation Procedure -- 10.3 Examples -- References -- Chapter 11 Viscous Flow Computation Using Navier-Stokes Equations.
11.1 Navier-Stokes Equations in the Unified Coordinates -- 11.2 The Angle-preserving Equation -- 11.3 Advantages of the g-equation Over the h-equation -- 11.4 Boundary Condition and Movement of Boundary Cells -- 11.5 Solution Strategies -- 11.6 Test Examples: Shock/Boundary Flow Interaction and Shock/Shock Interaction -- References -- Chapter 12 Applications of the Unified Coordinates to Kinetic Theory -- 12.1 Brief Introduction of Gas-Kinetic Theory -- 12.2 Gas-Kinetic BGK Model Under the Unified Coordinate Transformation -- 12.3 Numerical BGK-NS Scheme in a Moving Mesh System -- 12.4 Numerical Procedure -- 12.5 Numerical Examples -- 12.6 Conclusion -- References -- Chapter 13 Summary -- Appendix A Riemann Problem for 1-D Flow in the Unified Coordinate -- Nonlinearity of Characteristic Fields -- Smooth Solution -- Discontinuous Solutions -- Appendix B Computer Code for 1-D Flow in the Unified Coordinate.
Subject Fluid dynamics -- Mathematics
Numerical analysis
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Other name(s) Xu, Kun
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