Preface
Navier-Stokes Equations
Application of Computational Fluid Dynamics
Advantages of a Theoretical Calculation
1. FLUID DYNAMICS
1.1. Some useful formulas.
1.2. Fundamental Equations
1.4. Momentum Equation
1.5. Energy Equation
1.6. Equation of State
1.7. Vector Form of Equations
1.8. Orthogonal Curvilinear Coordinates
1.9. General transport equation
1.10. One-Way and Two-Way Coordinates
2. DISCRETIZATION METHODS
2.1.The Task
2.2. Taylor-Series Formulation
2.3. Control Volume Approach
2.4. The basic rules derived from a physical sense of control volume method
2.5. Convergence
2.7. Stability of a discretization scheme.
2.8. Convergence as a consequence of approximation and stability
2.9. Spectral analysis of the difference problem
2.10. Explicit, Crank-Nicolson, and Fully Implicit Schemes
2.11. TriDiagonal-Matrix Algorithm
2.12. Time-development method for steady state problems
Problems
3. NUMERICAL SOLUTION OF THE NAVIER-STOKES EQUATIONS
3.1. Desirable Numerical Properties
3.2. MacCormack Explicit Method
3.3. The finite volume approximation of Navier-Stockes equations
3.5. Jacobian matrices, eigenvalues, eigenvectors
3.6. Explicit and implicit Finite Volume Schemes
3.7. Viscous fluxes
3.8. Ways to improve the numerical method
Problems
4. SOLUTION OF SYSTEMS OF LINEAR EQUATIONS WITH BLOCK COEFFICIENTS
4.1. Finite approximating difference/volume equation
4.2. Gauss-Seidel iteration method
4.3. Approximate Factorization (AF)
4.4. Modified Approximate Factorization (MAF)
4.5. Block TriDiagonal-Matrix Algorithm
5. BOUNDARY CONDITIONS
5.1. Characteristics. Riemann's invariants.
5.2. Types of boundary conditions
5.2.1. INLET
5.2.2. OUTLET
5.2.3. FREE STREAM BOUNDARY
5.2.4. WALL
5.2.5. PLANE (LINE) of SYMMETRY
5.3. Ghost cells
5.3.1. Boundary conditions for inviscid fluxes
5.3.2. Viscous Boundary Condition
6. COMPUTATIONAL RESULTS
6.1. Supersonic jet at high exit static pressure ratio
6.2. Supersonic oxygen jet in high-temperature ambient.
6.3. Cold under-expanded and over-expanded air jets
6.4. Highly Under-Expanded Chemically Reacting Jets
6.5. Afterburning of exhaust plume.
REFERENCES