Computational Fluid Dynamics - Fall 2003

1. Computational Fluid Dynamics - Fall 2003 • The syllabus • Term project • CFD references (Text books and papers) • Course Tools • Course Web Site: http://twister.ou.edu/CFD2003 • Blackboard http://ou.blackboard.com • Computing Facilities available to the class (accounts info will be provided) • SOM Metlab workstations and OSCER (http://oscer.ou.edu) IBM Supercomputer • 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 usually analytical 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 Fluid Dynamics? • Analytical solutions exist only for a handful of typically simple problems • Much more flexible – each change of configurations, parameters • 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 than observations of both real and laboratory phenomena

8. Why Computational Fluid Dynamics? - Continued • We can perform realistic experiments on phenomena that are not possible to reproduce in reality, e.g., the weather • Much cheaper than laboratory experiments (e.g., crash test of vehicles, experimental launches of spacecrafts) • May be much environment friendly (testing of nuclear arsenals) • We can now use computers to DISCOVER new things (drugs, sub‑atomic particles, storm dynamics) much quicker • Computer models can predict, such as the weather.

9. An Example Case for CFD – Thunderstorm Outflo/Density Current Simulation

10. Thunderstorm Outflow in the Form of Density Currents

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

12. T=12 Positive Internal Shear g=1 Negative Internal Shear g=-1 No Significant Circulation Induced by Cold Pool

13. 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.

14. Difficulties with CFD • Typical equations of CFD are partial differential equations (PDE) that 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 between scales in atmospheric flows and most CFD problems. ENERGY TRANSFERS

15. Difficulties with CFD • 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!!

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