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 Fixed Coordinates 2.3 Conservation Law Equations in Moving Coordinates 2.4 Integral Equations versus Partial Di?erential 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 3.2 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 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 Lawfor Smooth FlowComputation 4.4 The Unified Computer Code 4.5 Cure of Defects of Eulerian and Lagrangian Computation by the UC Method 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 E?ects 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 Appendix B Computer Code for 1-D Flow in the Unified Coordinate
京公网安备 11010102004214号