Computational Fluid Dynamics - Fall 2001

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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.edu8900
• Computing Facilities
• Cray J90 and SOM workstations
• Unix and Fortran Helps Consult Links at CFD
  Home page

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Introduction Principle of Fluid Motion

• Mass Conservation
• Newtons 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

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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

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Theoretical FD

• Science for finding solutions of governing
  equations in different categories and studying
  the associated approximations / assumptions

h d/2,
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Experimental FD

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

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Computational FD

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

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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

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An Example Case for CFD Density Current
Simulation
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Thunderstorm Outflow in the Form of Density
Currents
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Positive Internal Shear
g1
Negative Internal Shear
g-1
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Positive Internal Shear
T12
g1
Negative Internal Shear
g-1
No Significant Circulation Induced by Cold Pool
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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.
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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!!

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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.