Introduction to Computational Fluid Dynamics

In This Section


This introductory course will prepare you for a career in the rapidly expanding field of computational fluid dynamics.

How You Will Benefit From This Course:

  • Learn the terminology used in CFD.
  • Learn and experience how applications of various numerical schemes to scalar model partial differential equations are used to illustrate the different aspects of CFD.
  • Improve your understanding of the limitations and advantages of CFD.
  • Discover why CFD is the tool for fluid flow simulations and prediction that has virtually none of the inherent limitations of other simulation techniques.


Key Topics:

  • Classification of Partial Differential Equations (PDEs)
  • Finite-Difference Equations
  • Parabolic Equations
  • Stability Analysis
  • Elliptic Partial Differential Equations
  • Hyperbolic Partial Differential Equations
  • Scalar Representation of the Navier-Stokes Equations
  • Incompressible Navier-Stokes Equations


Who Should Attend:

This course is designed for engineers, scientists, and technical managers who are interested in learning the fundamentals and principles of CFD. The objectives of this course are to provide simple, but in-depth explanations of solution schemes. The content of this course is equivalent to one-semester course offered to upper level undergraduates or first year graduate students. Prior introductory courses in fluid mechanics and partial differential equations are also helpful.

Type of Course: Instructor-Led Short Course

Course Level: Fundamentals

Course scheduling available in the following formats:

  • Distance Learning/Home Study Course


Course Length: 5 months

AIAA CEU's available: no

  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


Klaus A. Hoffmann is the Marvin J. Gordon Distinguished professor of aerospace engineering at Wichita State University. He has conducted extensive research in the areas of Navier-Stokes equations, Euler equations, parabolized Navier-Stokes equations, grid generations, boundary layer computations, turbulence models, and aerodynamic environment of reentry vehicles and hypervelocity projectiles. He has received excellent evaluations from more than 986 professionals who have taken this series of distance learning courses.