统一坐标系下的计算流体力学

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： 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