Computational Fluid Dynamics - Fall 2007 The syllabus CFD references (Text books and papers) Course Tools Course Web Site: Computing Facilities available to the class (account info will be provided) OSCER ( Topdawg Linux Supercomputerhttp://oscer.ou.edu Unix and Fortran Helps – Consult Links at CFD Home page

Introduction – Principle of Fluid Motion 1.Mass Conservation 1.Conservation of air mass 2.Conservation for other material quantities (e.g., CO 2 or water vapor in atmosphere) 2.Newton’s Second of Law (equations of motion) 3.Energy Conservation (e.g., temperature equation) 4.Equation of State for Idealized Gas 5.Other equations 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 – find analytical solutions Experimental – collect data from laboratory or field experiments Newer Approach Computational - CFD emerged as the primary tool for engineering design, environmental modeling, weather prediction, oil reservoir simulation and prediction, nuclear weapon testing, among many others, thanks to the advent of digital computers

Theoretical FD Science for finding usually analytical 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 Fluid Dynamics? Analytical solutions exist only for a handful of typically simple problems Much more flexible – easy change of configurations, parameters Can control numerical experiments and perform sensitivity studies, for both simple and complex systems or problems Can study something that is not directly observable (e.g., black holes of the universe or the future climate) because of the spatial and/or temporal scale of the problem. Computer solutions provide a more complete sets of data in time and space than observations of both real and laboratory phenomena

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

An Example Case for CFD – Thunderstorm Outflow/Density Current Simulation

Thunderstorm Outflow in the Form of Density Currents

 =1  =-1 Negative Internal Shear Positive Internal Shear

 =1  =-1 Negative Internal Shear Positive Internal Shear T=12 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, ARPS 48 h Forecast at 6 km Resolution Shown are the Composite Reflectivity and Mean Sea-level Pressure.

Movie of WRF 2 km forecast v.s. observations during Spring 2007 Forecast Experiment (Xue et al. 2007)Xue et al minute time intervals

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 ocean and 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 (against theoretical understanding and limited measurement data)! 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 among scales.

Difficulties with CFD The initial conditions of given problems often contain significant uncertainty – such as that of the atmosphere – because they can’t be measured with 100% accuracy 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 (Petascale Computing Systems to be built – first at NCSA) Faster networks Better desktop computers Better programming tools and environment Better visualization tools Better understanding of dynamics / predictabilities etc.