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- Introduction
- Governing Equation
- Derivation of Finite Difference Equations
- Solution Methods of Finite Difference Equations
- Incompressible Viscous Flows via Finite Difference Methods
- Compressible Flows via Finite Difference Methods
- Finite Volume Methods via Finite Difference Methods
- Introduction to Finite Element Methods
- Finite Element Interpolation Functions
- Linear Problems
- Steady-State Problems – Standard Galerkin Methods
- Two-Dimensional Elliptic Equations
- Boundary Conditions in Two Dimensions
- Nonlinear Problems/Convention-Dominated Flows
- Incompressible Viscous Flows via Finite Element Methods
- Compressible Flows via Finite Element Methods
- Miscellaneous Weighted Residual Methods
- Finite Volume Methods via Element Methods
- Relationships between Finite Differences and Finite Elements and Other Methods
- Structured Grid Generation
- Unstructured Grid Generation
- Adaptive Methods
- Computing Techniques
- Applications to Turbulence
- Applications to Chemically Reactive Flows and Combustion
- Applications to Acoustics
- Applications to Combined Mode Radiative Heat Transfer
- Applications to Multiphase Flows
- Applications to Electromagnetic Flows
- Applications to Relativistic Astrophysical Flows
- Appendix A Three-Dimensional Flux Jacobians
- Appendix B Gaussian Quadrature
- Appendix C Two Phase Flow – Source Term Jacobians for Surface Tension
- Appendix D Relativistic Astrophysical Flow Metrics, Christoffel Symbols, and FDV Flux and Source Term Jacobians