Advanced Computational Fluid Dynamics

In This Section

How You Will Benefit From This Course:

  • Improve your understanding of various aspects of computational fluid dynamics, its limitations and advantages.
  • Become familiar with the transformation of the equations of fluid motion from physical space to computational space and numerical algorithms for the solution of Euler, parabolized Navier-Stokes, and Navier-Stokes equations.
  • Learn the fundamentals of the unstructured grids and finite volume schemes.

Key Topics:

  • Grid-Generation-Structured Grids
  • Transformation of the Equations of Fluid Motion from Physical Space to Computational Space
  • Euler Equations
  • Parabolized Navier-Stokes Equations
  • Navier-Stokes Equations
  • Grid-Generation-Unstructured Grids Incompressible Navier-Stokes Equations
  • Finite Volume Schemes

Who Should Attend:

This course is designed for engineers, scientists, and technical managers who are interested in development and/or implementation of available CFD codes. The aim of this course is to extend the concepts of numerical schemes to a system of equations typically expressed in a vector form. The content of this course is equivalent to a one-semester graduate course. Furthermore, you must have had an introductory course in CFD, e.g., the AIAA Introduction to Computational Fluid Dynamics course. Access to a high-end PC, workstation, or a mainframe computer, along with a FORTRAN compiler and graphics, is necessary for applications.

Course Information:

Type of Course: Instructor-Led Short Course
Course Level: Advanced

Course scheduling available in the following format:

  • Distance Learning/Home Study
  • On-site Course

Course Length: 5 months for the home study course; 2 days for on-site course
AIAA CEU's available: yes, only for on-site course.


I. Grid-Generation-Structured Grids 

A. Algebraic grid generation techniques Metrics and the Jacobian of transformation Partial differential equations techniques Elliptic, parabolic, and hyperbolic grid generators
B. Coordinate system control
II.Transformation of the Equations of Fluid Motion from Physical Space to Computational Space
A. Generalized coordinate transformation
B. Navier-Stokes equations
C. Euler equations
D. Parabolized Navier-Stokes equations
E. Inviscid and viscous Jacobians
III.Euler Equations
A. Numerical schemes
B. Flux vector splitting
C. Implicit formulations
D. Explicit formulations
E. Initial and boundary conditions
F. Applications
G. Block-tridiagonal system of equations
H. Characteristics variables
IV.Parabolized Navier-Stokes Equations
A. Streamwise pressure gradient
B. Numerical algorithm
C. Shock fitting procedure
V. Navier-Stokes Equations
A. Navier-Stokes equations for compressible flows
B. Numerical algorithms
C. Initial and boundary conditions
D. Extension to three dimensions
VI.Grid-Generation-Unstructured Grids
A. Domain triangulation
B. The advancing front method
C. Delaunay method
VII.Finite Volume Schemes
A. Cell centered schemes
B. Nodal point schemes
C. Flux vector-splitting scheme



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.