Part I: Fundamentals
Introduction
General Remarks
Comparison of Experimental, Theoretical, and Computational Approaches
Historical Perspective
Partial Differential Equations
Introduction
Physical Classification
Mathematical Classification
Well-Posed Problem
Systems of Partial Differential Equations
Other PDEs of Interest
Problems
Basics of Discretization Methods
Introduction
Finite Differences
Difference Representation of Partial Differential Equations
Further Examples of Methods for Obtaining Finite-Difference Equations
Finite-Volume Method
Introduction to the Use of Irregular Meshes
Stability Considerations
Problems
Application of Numerical Methods to Selected Model Equations
Wave Equation
Heat Equation
Laplace's Equation
Burgers' Equation (Inviscid)
Burgers' Equation (Viscous)
Concluding Remarks
Problems

Part II: Application of Numerical Methods to the Equations of Fluid Mechanics and Heat Transfer Governing Equations of Fluid Mechanics and Heat Transfer
Fundamental Equations
Averaged Equations for Turbulent Flows
Boundary-Layer Equations
Introduction to Turbulence Modeling
Euler Equations
Numerical Methods for Inviscid Flow Equations
Introduction
Method of Characteristics
Classical Shock-Capturing Methods
Flux Splitting Schemes
Flux-Difference Splitting Schemes
Multidimensional Case in a General Coordinate System
Boundary Conditions for the Euler Equations
Methods for Solving the Potential Equation
Transonic Small-Disturbance Equations
Methods for Solving Laplace's Equation
Problems
Numerical Methods for Boundary-Layer-Type Equations
Introduction
Brief Comparison of Prediction Methods
Finite-Difference Methods for Two-Dimensional or Axisymmetric Steady External Flows
Inverse Methods, Separated Flows, and Viscous-Inviscid Interaction
Methods for Internal Flows
Application to Free-Shear Flows
Three-Dimensional Boundary Layers
Unsteady Boundary Layers
Problems
Numerical Methods for the "Parabolized" Navier-Stokes Equations
Introduction
Thin-Layer Navier-Stokes Equations
"Parabolized" Navier-Stokes Equations
Parabolized and Partially Parabolized Navier-Stokes Procedures for Subsonic Flows
Viscous Shock-Layer Equations
"Conical" Navier-Stokes Equations
Problems
Numerical Methods for the Navier-Stokes Equations
Introduction
Compressible Navier-Stokes Equations
Incompressible Navier-Stokes Equations
Grid Generation
Introduction
Algebraic Methods
Differential Equation Methods
Variational Methods
Unstructured Grid Schemes
Other Approaches
Adaptive Grids
Problems
Appendix A: Subroutine for Solving a Tridiagonal System of Equations
Appendix B: Subroutines for Solving Block Tridiagonal Systems of Equations
Appendix C: Modified Strongly Implicit Procedure
Nomenclature
References
Index