1. EULAG-MHD: simulation of global solar dynamo
Piotr K Smolarkiewicz*,
*National Center for Atmospheric Research, Boulder, Colorado, U.S.A.

2. Toroidal component of B in the uppermost portion of the stable layer underlying the convective envelope at r/R≈ 

3. Mihai Ghizaru, Paul Charbonneau, PK Smolarkiewicz, MAGNETIC CYCLES IN GLOBAL LARGE-EDDY SIMULATIONS OF SOLAR CONVECTION, The Astrophysical Journal Letters, 715:L133–L137, 2010; R. Bhattacharyya, B.C. Low, and P.K. Smolarkiewicz On spontaneous formation of current sheets: Untwisted magnetic fields. PHYSICS OF PLASMAS 17, Etienne Racine, P Charbonneau, M Ghizaru, Amelie Bouchat, PK Smolarkiewicz, ON THE MODE OF DYNAMO ACTION IN A GLOBAL LARGE-EDDY SIMULATION OF SOLAR CONVECTION, The Astrophysical Journal, 735:46 (22pp), 2011; Patrice Beaudoin, P. Charbonneau, E. Racine, P.K. Smolarkiewicz, Torsional Oscillations in a Global Solar Dynamo, Solar Physics (2012) in press Piotr K Smolarkiewicz, Paul Charbonneau EULAG, a Computational Model for Multiscale Flows: an MHD Extension Journal of Computational Physics, submitted

4. Standard anelastic equations of solar magnetohydrodynamics
Brun, Miesch & Toomre,

5. Elemental EULAG formulation
; Bauer, 1908

6. Coordinate dependent form

7. Coordinate dependent form

8. Numerical approximations; background
 elliptic problems for potentials 

9. Specialized MHD implementation
Hydrodynamic block

10. Magnetic block
Thermodynamics

11. Model setups
stable up to
and unstable stable aloft

12. Power of ILES

14. Magnetic cycles

15. Mode of large-scale dynamo action

17. Remarks
Notwithstanding some departures from the real solar climate, global MHD simulations of solar-like cycles have landed.
EULAG-MHD offers an outstanding virtual MHD laboratory allowing to address quantitatively a number of questions that could until now only be speculated
upon on the basis of simplified model formulations.
There is much to be learned. For example, our calculations suggest that the entire magnetic variability involves less then 10% of solar luminosity  connection to physics of other “dissipative structures” (QBO, MJO, ….)
Numerics-wise we have learned that work of elliptic solvers is adaptive rather than additive

18. Deriving the entropy equation

19. What is A operator?
Multidimensional positive definite advection transport algorithm (MPDATA):