Generation of Artificial Data in Support of SDO-HMI

Nagi N. Mansour, NASA ARC

Alan Wray, NASA ARC

Thomas Hartlep, Stanford CTR

Alexander Kosovichev, Stanford HEPL

Thomas Duvall, NASA GSFC

Mark Miesch, UCAR

Two efforts in progress:

(1) Direct simulation of wave propagation in solar interior

(2) Large-eddy simulation of the near-surface convection zone

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∂t ′ ρ = −Φ

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∂t Φ = −∇2 c 2 ′ ρ ( ) +1

r2∂r (r

2g ′ ρ )

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+ f

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−σ ′ ρ

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−σΦ

Randomforcing

DampingLayer aboveSurface

Wave equation

Equations

Direct Simulation of Wave Propagation in the Solar Interior

• Spherical harmonics, and Basis-Spline in radial direction

• Resolution in all directions adjustable with r• Treatment of coordinate singularity by

enforcing regularity condition at the center

• Non-reflecting boundary by means of a damping layer at the top

• Temporally random forcing of each spherical harmonics mode

NumericalMethod

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′ ρ l,m (r) = r lP(r2)

Example of B-Splines

OscillationPowerSpectraradial-symmetricSound Speed of aStandard Solar Model

with gravity term

without gravity term

StellarBox

• Rectangular geometry

• 50 50 43 Mm

• Compressible, radiation-hydro equations

• LTE radiation, 14 ray angular quadrature

• Non-ideal (tabular) EOS; tabular, binned opacity

• 4th order Padé derivatives

• 3rd (or 4th) order Runge-Kutta in time

• No-penetration, hydrostatic-pressure b.c.’s

• MPI parallelization

StellarBox MPI code

500x500x500

0

2

4

6

8

10

12

0 100 200 300 400 500 600

Number of processors

Mega-updates/sec

Scaling results on Columbia

Current status

• 500500500 on 100 processors (typically)• ~7-8 hour runs• 700-800 steps/run• Also used on brown dwarf stars

Vertical velocity in an x-z plane

QuickTime™ and aBMP decompressor

are needed to see this picture.

Enstrophy ( ||2 ) in an x-z plane

QuickTime™ and aBMP decompressor

are needed to see this picture.