Computational Fluid Dynamics( And Visualization Thereof )

John T. Bell

CS 526 at UIC

12 February 2004

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, . . .

Automotive Aerodynamics . . .

. . . And Interior Comfort . . .

. . . And Engine Conditions

Process Engineering

Aeronautics

NASA Ames’ Virtual Windtunnel

HVAC

VTK Examples

So How is CFD Calculated ?

Classic Differential Equations

• Navier-Stokes:

• Continuity:

• Cons. Energy:

21 1u u u P u Ft

( ) 0v n dA dVt

( )sWWQ P

e v n dA e dVdt dt dt t

Fourth Order Runge-Kutta

1

12

23

4 3

531 2 41

( , )

( , )2 2

( , )2 2

( , )

( )6 3 3 6

n n

n n

n n

n n

n n

k hf x y

h kk hf x y

h kk hf x y

k hf x h y k

kk k ky y O h

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.

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”.