Fundamentals of Computational Fluid Dynamics

1. Introduction.- 2. Conservation Laws and the Model Equations.- 3. Finite-Difference Approximations.- 4. The Semi-Discrete Approach.- 5. Finite-Volume Methods.- 6. Time-Marching Methods for ODE’S.- 7. Stability of Linear Systems.- 8. Choosing a Time-Marching Method.- 9. Relaxation Methods.- 10. Multigrid.- 11. Numerical Dissipation.- 12. Split and Factored Forms.- 13. Analysis of Split and Factored Forms.- Appendices.- A. Useful Relations from Linear Algebra.- A.1 Notation.- A.2 Definitions.- A.3 Algebra.- A.4 Eigensystems.- A.5 Vector and Matrix Norms.- B. Some Properties of Tridiagonal Matrices.- B.1 Standard Eigensystem for Simple Tridiagonal Matrices.- B.2 Generalized Eigensystem for Simple Tridiagonal Matrices.- B.3 The Inverse of a Simple Tridiagonal Matrix.- B.4 Eigensystems of Circulant Matrices.- B.4.1 Standard Tridiagonal Matrices.- B.4.2 General Circulant Systems.- B.5 Special Cases Found from Symmetries.- B.6 Special Cases Involving Boundary Conditions.- C. The Homogeneous Property of the Euler Equations.