Computational Fluid Dynamics - Fall 2001 The syllabus Term project CFD references Course Tools Course Web Site: http://twister.ou.edu/CFD2001 University CourseNet: http://coursenet.ou.edu. College of Geoscience WebCT site: http://www.gcn.ou.edu:8900 Computing Facilities Cray J90 and SOM workstations Unix and Fortran Helps – Consult Links at CFD Home page

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

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

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

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

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

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

An Example Case for CFD – Density Current Simulation

Thunderstorm Outflow in the Form of Density Currents

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

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

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.

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!!

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.