an immersed boundary method in wrf for complex mountainous ...dynamics/materhorn/pdf/chow... ·...
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An immersed boundary method in WRF for complex mountainous terrain
Tina Katopodes Chow1, Jingyi Bao1, Jason Simon1, Katherine A. Lundquist2
1Civil and Environmental Engineering University of California, Berkeley
2Lawrence Livermore National Laboratory
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Overview p WRF-IBM for mesoscale to microscale
n Terra incognita p Log law implementation
n Method development and testing p Application to Granite Mountain
n Preliminary results
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Terra incognita
p Flow features “partially” resolved
p Also -> terrain features “partially” resolved
Meso-scale L ~ 2-2000 km
LES L < 2 km
“Terra incognita” Wyngaard (JAS 2004)
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What we are doing p Weather and
Research Forecasting (WRF) model n Mesoscale to
microscale p One tool for all
scales n Improved turbulence
models for LES n Immersed boundary
method (IBM) for steep terrain
Granite Mountain, Utah
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Increasing resolution steeper slopes 3 km, max slope ~4° 1 km, max slope ~14°
300 m, max slope ~28° 100 m, max slope ~32°
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Terrain slope limit
Terrain-following coordinates p Horizontal pressure
gradient errors n 45° limit, usually ~30° starts
causing problems (e.g. Mahrer 1984)
p Grid aspect ratio limitations
p Numerical stability
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Ghost-cell immersed boundary method
Immersed boundary
Ghost point
Nearest neighbors
Enforce conditions on the immersed boundary
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IBM - Boundary reconstruction p IBM implemented in WRF p 2 different interpolation algorithms p Handles highly complex topography
Lundquist et al. MWR 2010, 2012
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Seamless grid nesting l Mesoscale to microscale l Must switch from WRF to IBM-WRF l When to switch?
l Resolution, steepness, aspect ratio, turbulence closure
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Complex terrain applications p Current implementation
for no-slip n Good for urban
environments at ~1 m resolution
p Need log law wall stress for complex terrain
IBM-WRF for Oklahoma City
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WRF implementation of log law p Momentum equation in U direction
p Requires gradient in
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WRF implementation of log law
…
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IBM – log law implementation
0=== surfacesurfacesurface wvuuU
nU
ozhzw
!
!
2
1ln
0ˆ
⎟⎟
⎠
⎞
⎜⎜
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⎛−=
=⋅
−
κµτ
No-Slip Shear Stress Reconstruction
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Test cases p Flat terrain p Idealized hill p Granite Mountain
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Validate with simple setup p Small grid changes can make big
difference p Height of first grid cell above wall
determines slope
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uG
uI τW
3D log law implementation
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τG
τI τW
3D log law implementation
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Idealized hill p Goal: match WRF
and WRF-IBM results p Notes about log law:
n WRF implements d/dz instead of d/dn
n WRF results depend strongly on choice of dz
Red – terrain following coordinates (WRF)
Blue – Immersed Boundary Method (IBM-WRF)
Lundquist et al. 2010, 2012
No slip conditions
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Granite Mountain – IBM test case
Granite Mountain, Utah
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Preliminary simulations p IBM-WRF can run at least 60m resolution
n Standard WRF blows up at ~300m resolution for 3D Granite Mountain
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MATERHORN: addressing challenges in the “Terra incognita”
p Steep topography p Turbulence modeling p Land-surface fluxes – similarity theory
Meso-scale L ~ 2-2000 km
LES L < 2 km
“Terra incognita” Wyngaard (JAS 2004)
IBM-WRF
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Take home messages p There exists a “Terra
incognita” for terrain p Log law implementation very
sensitive to resolution near the ground
p Ongoing work: stable boundary layer flows over Granite Mountain
p Funding thanks to the ONR MURI MATERHORN project