Initial Analysis of the Large-Scale Stein-Nordlund

Simulations Dali Georgobiani

Formerly at:

Center for Turbulence Research Stanford University/ NASA

Presenting the results of

Bob Stein (MSU) & Åke Nordlund (Denmark)with

David Benson (MSU)Stanford, August 19, 2005

The Old CodeStein – Nordlund RHD 3D simulations• Compressible (M)HD equations• LTE non-gray radiation transfer• Realistic EOS and opacities

No free parameters (except for diffusion model). Wave excitation and damping occur naturally. There is an excellent correspondence between the code results and observations.

The New CodeStein – Nordlund RHD 3D simulations• Conservative Compressible (M)HD equations• LTE non-gray radiation transfer• Realistic EOS and opacities

No free parameters (except for diffusion model). Wave excitation and damping occur naturally. There is an excellent correspondence between the code results and observations.

€

∂ρ∂t

= −∇ • ρu

€

∂ρui∂t

= −∂

∂x jρuiu j + Pδij + ρυ

∂ui∂x j

+∂u j∂x i

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥+ ρgi + J × B( )i

€

∂ρe∂t

= −∇ • ρeu− P∇ • u+ ρν∂ui∂x j

+∂u j∂x i

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

2

+ηJ 2 +Qrad

€

∂B∂t

= −∇ × E, E = −u× B +ηJ, J = ∇ × B /μ0

48 Mm

48

Mm

20

Mm

Numerical Convection

Oscillations are naturally driven by numerical turbulent convection

Convection

Oscillations

The New Code

• Supergranulation scale simulations• Currently 48 Mm x 48 Mm x 20 Mm• Resolution 100 km horizontally, 12 – 75 km

vertically

• Numerical Method: Staggered variables Spatial differencing: 6th order centered finite

difference Time advancement: 3rd order Runge-Kutta

Radiation Treatment

• LTR

• Non-grey, 4 bin multigroup

Equation of State• Tabular EOS

Includes ionization, excitation

H, He, H2, other abundant elements

Boundary Conditions• Density: top hydrostatic, bottom logarithmic

• Velocity: symmetric (normal derivative = 0)

• Energy (per unit mass): top – slowly evolving average, bottom – fixed energy in inflows

Initialization• Start from existing 12x12x9 Mm simulation

• Extend adiabatically to 20 Mm and relax for a solar day to develop structures

• Double horizontally + small fraction of stretched fluctuations to remove symmetry

• Relax to develop large-scale structures

Energy Fluxes

Mean AtmosphereTemperature, Density and

Pressure

Mean AtmosphereIonization of He, He I and He

II

Convective Flux

Old code, vertical velocity

NEW CODE

VerticalVelocity

NEWCODE

HorizontalVelocity Divergence

New code (movie by Bob Stein)

Old code

New code (movie by Bob Stein)

Old code New code

ω−k diagram

Summary - Advantages

Time – Distance calculations Acoustic holography MHD version: pores, sunspots? Spectra? Mode asymmetries?

Future Plans

Large domain – supergranulation scale Deep - includes lower turning points Fast code (parallelizes well)