# Advanced Computational Fluid Dynamics

#### Overview:

• 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 Length - Variable (1-4 days)

Outline

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

Materials

Instructors

TBD