2. What is CFD, and Who Cares ?
• Simply put, CFD is the calculation of
properties of a flowing fluid.
• Practical problems may include energy flow,
chemical reactions, phase changes, …
• Domain is often ( irregular ) 3D, plus time.
• Results may be scalar, but more often are n-D
• Relevant industries include automotive,
chemical processing, aerospace, HVAC, . . .
12. Classic Differential Equations
• Navier-Stokes:
• Continuity:
• Cons. Energy:
2
1 1
u
u u P u F
t
( ) 0
v n dA dV
t
( )
s
W
W
Q P
e v n dA e dV
dt dt dt t
13. Fourth Order Runge-Kutta
1
1
2
2
3
4 3
5
3
1 2 4
1
( , )
( , )
2 2
( , )
2 2
( , )
( )
6 3 3 6
n n
n n
n n
n n
n n
k hf x y
h k
k hf x y
h k
k hf x y
k hf x h y k
k
k k k
y y O h
14. Conclusions
• Computational Fluid Dynamics is an important
tool in many branches of science and engineering.
• Results are typically n-D, over 3-D plus time.
• CFD calculations require simultaneous solution of
many sets of differential equations, typically
involving 4th order Runge-Kutta in 3-D space.
• Visualization of CFD data is an important and
challenging problem, requiring clever use of all
available visualization tools and skills.
15. References
• Fluent Inc.: Http://www.fluent.com
• Schulz, Martin et. al.: “Interactive Visualization of Fluid
Dynamics Simulations in Locally Refined Cartesian
Grids”. IEEE, 1999.
• NASA: http://www.nas.nasa.gov/Research/Tasks/
applications.html and http://www.nas.nasa.gov/Research/
Reports/ Techreports/1992/HTML/RNR-92-013.html
• Schroeder et. al.: “The Visualization Toolkit, 3rd Ed.”
• SDSC: http://www.sdsc.edu/Publications/GCequations/
• Welty, Wicks, & Wilson, “Fundamentals of Momentum,
Heat, and Mass Transfer, 2nd Ed.”, Wiley, 1976.
• Press, William et. al.: “Numerical Recipes in C”.
