High Resolution Simulation, Modeling and Characterization of Optical Turbulence

1
High Resolution Simulation, Modeling and
Characterization of Optical Turbulence

• D. Scott McRae, Hassan A. Hassan
• Xudong Xiao
• N.C. State University
• 25 September 2003

2
Outline

• Objective and Timeline
• Numerical resolution and turbulence scales
• Adaptive mesh algorithm and examples
• Optical turbulence model
• Progress to date
• Preliminary results
• Conclusion and acknowledgements
• Future Work

3
Objective

• To improve the simulation, modeling and
  characterization of optical turbulence
• Use dynamic mesh adaptation to increase shear
  layer resolution in selected regions imbedded in
  mesoscale weather models
• Improve subgrid scale (SGS) turbulence
  parametization by employing RANS models derived
  from the exact Navier-Stokes equations

4
Timeline

• Current capability-
• Mesoscale weather codes 5km resolution and
  models based on dimensional considerations and
  statistical correlation of measurements.
• Near-term goal-
• LES scale simulation of 10 to 100m by use of
  dynamic adaptivity in imbedded weather model
  region (nest) and a physically based RANS SGS
  model

5
Timeline

• Distant goal (after advances in computational
  power and understanding of the relevant physics)-
• Direct computation of from real time
  execution of highly resolved ( 1m) 4D weather
  model with advanced SGS model

6
Resolution Issues

• The difference mesh acts as a band-pass filter,
  with resolved wave numbers
• where the domain is 2L in extent with mesh
  spacing of

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Resolution Issues
For a wind of 30 m/s, a mesh of the spacing noted
would resolve these frequencies
10km 1km 50m
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Resolution Issues

• This implies that a mesh of 50m spacing with a
  physically correct subgrid model would be capable
  of simulating directly a significant percentage
  of the important turbulent scales
• This information would then be available for a
  direct calculation of , analogous to direct
  measurements

9
Resolution Issues

• Finally, the subgrid model would provide bias of
  the direct calculation results for those scales
  not simulated

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NCSU Adaptive Mesh Algorithm

• Relocates mesh nodes (r-refinement adaptation)
  dynamically and automatically
• General curvilinear transformation of the
  governing equations- permits adaptation in all
  three dimensions
• Temporal variation preserved
• Weight function based on any selected criteria
  for adaptation

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NCSU Adaptive Mesh Algorithm

• Has been applied to
• Various aerospace related simulations
• Regional Air Quality Modeling, in collaboration
  with Dr. Talat Odman of Georgia Institute of
  Technology
• Subgrid pollutant plume simulation ( with Dr.
  Odman )
• GIS Terrain information ( with Dr. Odman )
• Examples
• TVA area RAQM simulation
• GIS elevation adaptation

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• Adaptive algorithm examples
• T. Odman, Georgia Institute of Technology

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TVA Simulation

• Initial mesh spacing of 8 km
• Minimum spacing after adaptation 200m
• Weight function based on NO levels
• increased local resolution by factor of 40 in the
  vicinity of pollutant sources

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Mesh adapted to SAMI data 0700, June 7, 1995
(GIT)
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Plume structure as resolved by adaptive grid,
1700 June 7, 1995 (GIT)
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Surface elevation contours for the Island of
Hawaii (left) and a grid adapted to these
contours (right) (GIT)
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SGS Optical Turbulence Model

• Derive an SGS model using a Reynolds- averaged
  Navier- Stokes Formulation
• Provides a self-consistent approach for modeling
  unresolved scales
• Will address all relevant physics

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SGS Optical Turbulence Model

• Derive an expression for that can be
  deduced directly from the solution
• Remove empiricism inherent in dimensional
  considerations
• Will include influence of all scales
• Investigate impact of initial conditions
• Validate model by comparison with experiment

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Approach- SGS Model

• Improve parametization of SGS by using a hybrid
  Large Eddy Simulation/Reynolds Averaged
  Navier-Stokes (LES/RANS) Approach
• Coupling of the two approaches is accomplished by
  a flow dependent blending function

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Approach- SGS Model

• The RANS model is based on the full Navier-Stokes
  equations and consists of the following governing
  equations
• TKE (k, the turbulent kinetic energy)
• Enstrophy ( , the variance of vorticity)
• The temperature variance
• The dissipation of temperature variance

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Approach- SGS Model

• For optical turbulence, fluctuations of the index
  of refraction are well approximated by the
  relation
• or
• thus

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Approach- SGS Model

• Thus can be derived directly from the
  variance of potential temperature equation
• Since current approaches employ a structure
  function formulation, we can write
• where C is a constant

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Approach- SGS Model

• It can be shown from dimensional considerations
  that
• b is a constant,
• is the dissipation rate of temperature
  variance and
• is the dissipation rate of TKE
• All of these equations follow directly from the
  hybrid LES/RANS solution

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Approach- SGS Model

• With suitable assumptions for and
• where a is a constant, , are the eddy
  diffusivity and viscosity and L is the outer
  scale of turbulence. The models designated Dewan,
  CLEAR1, and HMASP99 differ in their expression
  for L.

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Code Development Progress

• MM5 selected for code development
• MM5 governing equations transformed to general
  curvilinear coordinate system
• NCSU turbulence model augmented to
  include temperature variance and its dissipation
• NCSU dynamic adaptive algorithm (DSAGA) and
  optical turbulence model installed to run in
  embedded MM5 nests

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Code Development Progress

• NCSU discontinuous mesh boundary algorithm and
  overlap condition compared for nest 4

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Preliminary Results

• MM5 Storm of the Century (SOTC) test case
  provides interesting conditions for evaluating
  adaptive algorithms
• Level 2 and 4 nest preliminary results obtained
  with dynamic 3-D mesh adaptation to local shear
  and vorticity
• Preliminary results demonstrate adaptation to
  shear layers due to terrain topology and also
  upper atmosphere shear
• Experiments still underway to determine best
  interface between 3 and 4 level nest

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Location of Nests
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SOTC results

• SOTC Initial horizontal mesh spacing in nest 2
  -30km
• Results for 720 minutes clock time
• MM5 even mesh nest 2 time step 80 sec.
• After adaptation, time step 15sec.
• Initial spacing in nest 4 - 3.33km
• Approximately linear reduction in time step

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Nest 2 Y-Z Surface Results
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Nest 2 Y-Z Surface Results
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Nest 2 Y-Z Surface Results
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Nest 2 X-Z Surface Results
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Nest 2 K surface Results
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Detail of Static Adaptation to Shear
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Conclusions

• Imbedded module with NCSUs dynamic, solution
  adaptive curvilinear mesh algorithm developed and
  installed in MM5
• New optical turbulence model developed from full
  Navier-Stokes equations and coded
• Contains all relevant physics
• Approach yields expressions that are
  valid without requiring the assumption of locally
  isotropic, homogeneous turbulence (I.e. does not
  require the Kolmogorov assumption)

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Conclusions

• Simultaneous dynamic adaptive resolution of
  surface, terrain topology induced, and upper
  shear layers demonstrated in preliminary large
  scale runs- exceeded current MM5 resolution goals
  in initial runs
• Adaptive fourth level nest demonstrated

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Acknowledgements

• Our thanks to the HEL- JTO and ARLWSMR for the
  initial funding to perform this research and to
  Dave Tofsted and Pat Haines of ARL for their
  guidance and many helpful conversations.

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Future Work

• Continue code development
• Check out optical turbulence model
• Need highly resolved, well documented data
• Code verification and exploration of adaptive LES
  scale resolution benefits
• 10m vertical and 10-100m horizontal resolution of
  local shear layers expected within 3 mos.
• Comparison of optical turbulence model results
  with experiment and other models
• Technology has many other applications

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SHOW STOPPER!

• ARLWSMR FUNDING FOR THIS RESEARCH WAS NOT RENEWED
  FOR THE SECOND YEAR
• RESIDUAL FUNDS WILL BE EXHAUSTED IN NOVEMBER
• WE MUST HAVE FUNDING TO CONTINUE THIS WORK!
• mcrae_at_eos.ncsu.edu
• 919 515 5244