1. 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

2. The Old Code Stein – 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.

3. The New Code Stein – 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. 48 Mm 20 Mm

4. Numerical Convection Oscillations are naturally driven by numerical turbulent convection Convection Oscillations

5. 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: 6 th order centered finite difference Time advancement: 3 rd order Runge-Kutta

6. Radiation Treatment LTR Non-grey, 4 bin multigroup Equation of State Tabular EOS Includes ionization, excitation H, He, H 2, other abundant elements

7. 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

8. Energy Fluxes

9. Mean Atmosphere Temperature, Density and Pressure

10. Mean Atmosphere Ionization of He, He I and He II

11. Convective Flux

12. Old code, vertical velocity

13. NEW CODE Vertical Velocity

14. NEW CODE Horizontal Velocity Divergence

15. New code (movie by Bob Stein)

16. Old code

17. New code (movie by Bob Stein)

18. Old codeNew code diagram

19. 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)