1. Computational Fluid Dynamics - Fall 2001
The syllabus
Term project
CFD references
Course Tools
Course Web Site:
University CourseNet:
College of Geoscience WebCT site:
Computing Facilities
Cray J90 and SOM workstations
Unix and Fortran Helps – Consult Links at CFD Home page

2. Introduction – Principle of Fluid Motion
Mass Conservation
Newton’s Second of Law
Energy Conservation
Equation of State for Idealized Gas
These laws are expressed in terms of mathematical equations, usually as partial differential equations.
Most important equations – the Navier-Stokes equations

3. Approaches for Understanding Fluid Motion
Traditional Approaches
Theoretical
Experimental
Newer Approach
Computational - CFD emerged as the primary tool for engineering design, environmental modeling, weather prediction, among others, thanks to the advent of digital computers

4. Theoretical FD
Science for finding solutions of governing equations in different categories and studying the associated approximations / assumptions;
h = d/2,

5. Experimental FD
Understanding fluid behavior using laboratory models and experiments. Important for validating theoretical solutions.
E.g., Water tanks, wind tunnels

6. Computational FD
A Science of Finding numerical solutions of governing equations, using high-speed digital computers

7. Why Computational FD
Analytical solutions exist only for a handful of typically simple problems
Can control numerical experiments and perform sensitivity studies, for both simple and complicated problems
Can study something that is not directly observable (black holes).
Computer solutions provide a more complete sets of data in time and space
We can perform realistic experiments on phenomena that are not possible to reproduce in reality, e.g., the weather
Much cheaper than laboratory experiments (crash test of vehicles)
May be much environment friendly (testing of nuclear arsenals)
Much more flexible – each change of configurations, parameters
We can now use computers to DISCOVER new things (drugs, sub‑atomic particles, storm dynamics) much quicker

8. An Example Case for CFD – Density Current Simulation

9. Thunderstorm Outflow in the Form of Density Currents

10. Positive Internal Shear
g=1
Negative Internal Shear
g=-1

11. Positive Internal Shear
g=1
Negative Internal Shear
g=-1
No Significant
Circulation Induced by
Cold Pool

12. Simulation of an Convective Squall Line in Atmosphere
Infrared Imagery Showing Squall Line at 12 UTC January 23, 1999.
ARPS 48 h Forecast at 6 km Resolution
Shown are the Composite Reflectivity and Mean Sea-level Pressure.

13. Difficulties with CFD
Typical equations of CFD are partial differential equations (PDE) the requires high spatial and temporary resolutions to represent the originally continuous systems such as the atmosphere
Most physically important problems are highly nonlinear ‑ true solution to the problem is often unknown therefore the correctness of the solution hard to ascertain – need careful validation!
It is often impossible to represent all relevant scales in a given problem ‑ there is strong coupling in atmospheric flows and most CFD problems. ENERGY TRANSFERS.
Most of the numerical techniques we use are inherently unstable ‑ creating additional problems
The initial condition of a given problem often contains significant uncertainty – such as that of the atmosphere
We often have to impose nonphysical boundary conditions.
We often have to parameterize processes which are not well understood (e.g., rain formation, chemical reactions, turbulence).
Often a numerical experiment raises more questions than providing answers!!

14. POSITIVE OUTLOOK New numerical schemes / algorithms
Bigger and faster computers
Faster network
Better desktop computers
Better programming tools and environment
Better understanding of dynamics / predictabilities
etc.