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Chapter 1 Introduction1£®1 CFD as Numerical Solution to Nonlinear Hyperbolic PDEs1£®2 Role of Coordinates in CFD1£®3 Outline of the BookReferencesChapter 2 Derivation of Conservation Law Equations2£®1 Fluid as a Continuum2£®2 Derivation of Conservation Law Equations in Fixed Coordinates2£®3 Conservation Law Equations in Moving Coordinates2£®4 Integral Equations versus Partial Differential Equations2£®5 The Entropy Condition for Inviscid Flow ComputationReferencesChapter 3 Review of Eulerian Computation for 1-D Inviscid Flow3£®1 Flow Discontinuities and Rankine-Hugoniot Conditions3£®2 Classification of Flow Discontinuities3£®3 Riemann Problem and its Solution3£®4 Preliminary Considerations of Numerical Computation3£®5 Godunov Scheme3£®6 High Resolution Schemes and Limiters3£®7 Defects of Eulerian ComputationReferencesChapter 4 I-D Flow Computation Using the Unified Coordinates4£®1 Gas Dynamics Equations Based on the Unified Coordinates4£®2 Shock-Adaptive Godunov Scheme4£®3 The Use of Entropy Conservation Law for Smooth Flow Computation4£®4 The Unified Computer Code4£®5 Cure of Defects of Eulerian and Lagrangian Computation by the UC Method4£®6 ConclusionsReferencesChapter 5 Comments on Current Methods for Multi-Dimensional Flow Computation5£®1 Eulerian Computation5£®2 Lagrangian Computation5£®3 The ALE Computation5£®4 Moving Mesh Methods5£®5 Optimal CoordinatesReferencesChapter 6 The Unified Coordinates Formulation of CFD6£®1 Hui Transformation6£®2 Geometric Conservation Laws6£®3 Derivation of Governing Equations in Conservation FormReferencesChapter 7 Properties of the Unified Coordinates7£®1 Relation to Eulerian Computation7£®2 Relation to Classical Lagrangian Coordinates7£®3 Relation to Arbitrary-Lagrangian-Eulerian Computation7£®4 Contact Resolution7£®5 Mesh Orthogonality7£®6 Unified Coordinates for Steady Flow7£®7 Effects of Mesh Movement on the Flow7£®8 Relation to Other Moving Mesh Methods7£®9 Relation to Mesh Generation and the Level-Set Function MethodReferencesChapter 8 Lagrangian Gas Dynamics8£®1 Lagrangian Gas Dynamics Equations8£®2 Weak Hyperbolicity8£®3 Non-Equivalency of Lagrangian and Eularian FormulationReferencesChapter 9 Steady 2-D and 3-D Supersonic Flow9£®1 The Unified Coordinates for Steady Flow9£®2 Euler Equations in the Unified Coordinates9£®3 The Space-Marching Computation9£®4 Examples9£®5 3-D FlowReferencesChapter 10 Unsteady 2-D and 3-D Flow Computation10£®1 Summary of Solution to the 2-D Euler Equations Using the Unified Coordinates10£®2 Computation Procedure10£®3 ExamplesReferencesChapter 11 Viscous Flow Computation Using Navier-Stokes Equations11£®1 Navier-Stokes Equations in the Unified Coordinates11£®2 The Angle-preserving Equation11£®3 Advantages of the g-equation Over the h-equation11£®4 Boundary Condition and Movement of Boundary Cells11£®5 Solution Strategies11£®6 Test Examples£º Shock/Boundary Flow Interaction and Shock/Shock InteractionReferencesChapter 12 Applications of the Unified Coordinates to Kinetic Theory12£®1 Brief Introduction of Gas-Kinetic Theory12£®2 Gas-Kinetic BGK Model Under the Unified Coordinate Transformation12£®3 Numerical BGK-NS Scheme in a Moving Mesh System12£®4 Numerical Procedure12£®5 Numerical Examples12£®6 ConclusionReferencesChapter 13 SummaryAppendix A Riemann Problem for 1-D Flow in the Unified CoordinateAppendix B Computer Code for 1-D Flow in the Unified Coordinate