T he A coustic S un S imulator Computing medium- l data
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Transcript of T he A coustic S un S imulator Computing medium- l data
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The Acoustic Sun Simulator
Computing medium-l data
Shravan Hanasoge Thomas Duvall, Jr.
HEPL, Stanford University
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Why artificial data?
Validation of helioseismic techniques
Improve understanding of wave interaction with flow structures, sunspot-like regions etc. – the need for controlled experiments
Improving existing techniques based on this understanding
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generating the data…
Acoustic waves are excited by radially directed stochastic dipoles
Waves propagate through a frozen background state that can include flows, temperature perturbations etc.
The acoustic signal is extracted at the photospheric level of the simulation
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Computation of Sources Granulation acts like a spatial delta function,
exciting all medium-l the same way.
Use a Gaussian random variable to generate a uniform spherical harmonic-spectrum and frequency limited series in the spherical harmonic – frequency space
Transform to real space to produce uncorrelated sources
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Theoretical model
The linearized Euler equations with a Newton cooling type damping are solved
Viscous and conductive process are considered negligible (time scale differences)
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Computational model Horizontal derivatives computed spectrally
Radial derivatives with compact finite differences
Time stepping by optimized 5 stage LDDRK (Hu et al. 1996)
Parallelism in OpenMP and MPI
Model S of the sun as the al.) background state (Christensen-Dalsgaard, J., et
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Horizontal variations
Spherical Harmonic decomposition of variables in the horizontal direction
Horizontal derivatives are calculated in Spherical Harmonic space (expensive)
Gaussian collocated grid points in latitude and equally spaced in longitude
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Crazy density changes…
11 scale heights between r = 0.26 and r = 0.986
13 scale heights between r = 0.9915 and r =1.0005
Grid allocation method is a combination of log-density and sound-speed
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Radial variations
Interior radial collocation: constant acoustic travel-time between adjacent grid point
Near surface collocation: constant in log density
Sixth order compact finite differences in the radial direction
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Radial grid spacing
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Boundary conditions
Absorbing boundary conditions on the top and bottom
Implemented using a ‘sponge’
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Convective instabilities The outer 30% of the sun is convectively
unstable The near-surface (0.1% of the radius) is
highly unstable – start of the Hydrogen ionization zone
Modeling convection is infeasible Instability growth rates around 5 minutes;
corrupt the acoustic signal Solution: altered the solar model to render the
model stable
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Artificially stabilized model Convectively stable
Maintain cutoff frequencies
Smooth extension of the interior model S
Hydrostatic equilibrium
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Log power spectrum – 24 hour data cube. Simulation domain extends from the outer core to the evanescent region. Banded structure due to limited excitation spectrum.
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Validation I – eigen-modes
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Validation II – frequency shifts by constant rotation
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Traveltimes
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Acoustic Wave Correlations
Medium l data correlations Correlation from simulations
Note that signal-noise levels compare very well!
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Problems with radial aliasing….
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Linewidths and asymmetries
• Solar-like velocity asymmetry
• Asymmetry reduces at higher frequencies due to damping
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Computational efficiency
The usefulness of this method limited by the rapidity of the computation
Currently, 1 seconds of computational time to advance solar time by 1.3 second (at l~127 )
The hope is to achieve this ratio at high l
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Interpreting the data…
Motivation guiding the effort: differential studies of helioseismic effects
Datum: a simulation with no perturbations
Differences in helioseismic signatures of effects are expected to be mostly insensitive to the neglected physics
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Capabilities at present
L < 200 (spherical harmonic degree) –OpenMP
Tested for L ~ 341 (works efficiently) with the MPI version
Can simulate acoustic interaction with: Arbitrary flows Sunspot type perturbations (no magnetic fields) Essentially, perturbations in density, temperature, pressure
and velocities
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Current applications
Can we detect convection? Far-side imaging: validation Solar rotation: how good are our
estimates? Tachocline studies Meridional flow models: validation Line of Sight projection effects
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References for this work
Computational Acoustics in spherical geometry: Steps towards validating helioseismology, Hanasoge et al. ApJ 2006 (to appear in September)
Computational Acoustics, Hanasoge, S. M. 2006, ILWS proceedings