Chapter 1 Introduction 1.1 CFD as Numerical Solution to Nonlinear Hyperbolic PDEs 1.2 Role of Coordinates in CFD 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 FixedCoordinates 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 InviscidFlow 3.1 Flow Discontinuities and Rankine-Hugoniot Conditions 3.2 Classification of Flow Discontinuities 3.3 Riemann Problem and its Solution 3.4 Preliminary Considerations of Numerical Computation 3.5 Godunov Scheme 3.6 High Resolution Schemes and Limiters 3.7 Defects of Eulerian Computation References Chapter 4 I-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 FlowComputation 4.4 The Unified Computer Code 4.5 Cure of Defects of Eulerian and Lagrangian Computation by theUC Method 4.6 Conclusions References Chapter 5 Comments on Current Methods for Multi-Dimensional FlowComputation 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 FunctionMethod 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 …… Chapter 10 Unsteady 2-D and 3-D Flow Computation Chapter 11 Viscous Flow Computation Using Navier-StokesEquations Chapter 12 Applications of the Unified Coordinates to KineticTheory Chapter 13 Summary Appendix A Riemann Problem for 1-D Flow in the UnifiedCoordinate Appendix B Computer Code for 1-D Flow in the Unified Coordinate
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