AIAA

The World's Forum for Aerospace Leadership

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The American Institute of Aeronautics and Astronautics (AIAA)

is the world's largest technical society dedicated to the global aerospace profession.

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    • AIAA Foundation
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    Course Outline

    Course Outline

    1. Classification of Partial Differential Equations (PDEs)
      1. Elliptic, parabolic, and hyperbolic PDEs
      2. System of first-order PDEs
      3. Sytem of second-order PDEs
      4. Initial and boundary conditions

    2. Finite-Difference Equations
      1. Derivation of finite-difference equations by Taylor series expansion
      2. Finite-difference formulations

    3. Parabolic Equations
      1. Explicit and implicit methods
      2. Applications
      3. Parabolic equations in two-space dimensions
      4. Approximate factorization
      5. Fractional step method
      6. Extension to three-space dimensions
      7. Consistency analysis of the finite-difference equations
      8. H. Linearization
      9. Irregular boundaries

    4. Stability Analysis
      1. Discrete perturbation stability analysis
      2. Von Neumann stability analysis
      3. Modified equation
      4. Artificial viscosity
      5. Error analysis
      6. Elliptic Partial Differential Equations

    5. Finite difference formulations
      1. Solution Procedures
      2. Applications

    6. Hyperbolic Partial Differential Equations

    7. Explicit and implicit formulations

    8. Splitting methods

    9. Characteristic equations

    10. Riemann invariants

    11. Linear damping

    12. Flux-corrected transport

    13. Monotone schemes

    14. TVD schemes

    15. Scalar Representation of the Navier-Stokes Equations

      1. Numerical algorithms
      2. Stability considerations
      3. Applications

    16. Incompressible Navier-Stokes Equations

      1. Primitive variable formulations
      2. Poisson equation for pressure
      3. Artificial compressibility
      4. D. Staggered grid
      5. E. Boundary conditions