Supergranulation-Scale Solar Convection Simulations

1. Supergranulation-Scale Solar Convection Simulations David Benson, Michigan State University, USA Robert Stein, Michigan State University, USA Aake Nordlund, Astronomical Observatory, NBIfAFG, Denmark AGU - SPD Conference May, 2005 New Orleans, LA

2. Overview • Purpose • Computational Methodology (brief) • Methods for Initializing Simulations • Preliminary Results: Simulations In-Progress • 50Mm x 50Mm x 20Mm (deep) simulations • Relaxing thermally and dynamically • Future Directions

3. Significance and Questions • Second Helium Ionization Zone • Separate the role of second helium ionization zone from the effect of the increasing scale height with depth • Helioseismology • Simulations serve as a tool for analyzing local helioseismic inversion techniques • Nature of the Surface Shear Layer • Development and Maintenance of the Magnetic Network

4. 20 Mm 50 Mm 50 Mm Computational Domain • 50Mm x 50Mm x 20Mm • 5003 grid points • Grid clustering near visible surface Computational Domain for the CFD Simulations of Solar Convection

5. Numerical Method • Spatial differencing • 6th-order centered f.d. • staggered • Time advancement • 3rd order Runga-Kutta • Equation of state • tabular • including ionization • H, He + abundant elements • Radiative transfer • 3D, LTE • 4 bin opacity distrib. fxn • Quenching

6. Computational Information • Fortran 90 • Parallelized - OpenMP • single parallel region • Michigan State University • 64 processor Altix • NCSA • IBM P690 • NASA Ames • Altix (128 processors) Objective: layer MPI on top of the OpenMP

7. Initialization Methods 24 Mm and 12 Mm Simulations • 12 Mm simulation (9 Mm deep) • well-relaxed • extended adiabatically to 20 Mm • Relax dynamics 12 Mm -- 20 Mm deep • Create 24 Mm wide box - and relax the following • 12 Mm stretched to 24Mm • generates large scale structure • 12 Mm doubled to 24 Mm

8. Initialization Methods Construction of 50 Mm Initial State • Stretch 12 Mm x 20 Mm to 50 Mm • Generates large scale structure • Breaks symmetry • Stretch 24 Mm x 20 Mm to 50 Mm • Generates intermediate level structure • Quadruple 12 Mm x 20 Mm to 50 Mm • Produces small scale structure Combine & Relax

9. Initialization Snapshots Components + Composite : Uz at 0.25 Mm Snapshots of methods + composite (?)

10. Initialization Snapshots Components + Composite : Uz at 17.3 Mm

11. Mean Atmosphere State Temperature, Density and Pressure

12. Mean Atmosphere State Ionization of H and He

13. Energy Fluctuation Need for Relaxation

14. Future Research Direction • Relax hydrodynamic simulations (further) • Implement magnetic field boundary conditions and add Coriolis force terms • Results will be available to help in answering questions about ... • Maintenance of magnetic network • f-plane rotation -- Coriolis force • Local helioseismic inversion techniques