Abstract
In this chapter, we show our development of numerical code. The detailed setting for calculations in the solar convection zone is introduced. The near-surface region (\(>\) \(0.98R_\odot \)) is included for the solar global convection calculation for the first time. Our new challenge for including the partial ionization effect of Hydrogen and Helium is explained. In order to deal with large number of CPUs in the huge parallel computer, we adopt efficient parallelizaion method, Peano-Hilbert space-filling curve and Yin-Yang grid. These are explained. Finally the method for analyzing the huge size data outputted by the calculations are introduced.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
J. Christensen-Dalsgaard, W. Dappen, S.V. Ajukov, E.R. Anderson, H.M. Antia, S. Basu, V.A. Baturin, G. Berthomieu, B. Chaboyer, S.M. Chitre, A.N. Cox, P. Demarque, J. Donatowicz, W.A. Dziembowski, M. Gabriel, D.O. Gough, D.B. Guenther, J.A. Guzik, J.W. Harvey, F. Hill, G. Houdek, C.A. Iglesias, A.G. Kosovichev, J.W. Leibacher, P. Morel, C.R. Proffitt, J. Provost, J. Reiter, E.J. Rhodes Jr., F.J. Rogers, I.W. Roxburgh, M.J. Thompson, R.K. Ulrich, The current state of solar modeling. Science 272, 1286–1292 (1996). doi:10.1126/science.272.5266.1286
H. Hotta, M. Rempel, T. Yokoyama, Y. Iida, Y. Fan, Numerical calculation of convection with reduced speed of sound technique. A&A 539, 30 (2012). doi:10.1051/0004-6361/201118268
A. Kageyama, T. Sato, “Yin-Yang grid”: An overset grid in spherical geometry. Geochem. Geophys. Geosyst. 5, 9005 (2004). doi:10.1029/2004GC000734
T. Matsumoto, Self-gravitational magnetohydrodynamics with adaptive mesh refinement for protostellar collapse. PASJ 59, 905 (2007)
M.S. Miesch, J.R. Elliott, J. Toomre, T.L. Clune, G.A. Glatzmaier, P.A. Gilman, Three-dimensional spherical simulations of solar convection. I. Differential rotation and pattern evolution achieved with laminar and turbulent states. ApJ 532, 593–615 (2000). doi:10.1086/308555
D. Mihalas, B.W. Mihalas, Foundations of Radiation Hydrodynamics (Oxford University Press, New York, 1984)
M. Rempel, M. Schüssler, M. Knölker, Radiative magnetohydrodynamic simulation of sunspot structure. ApJ 691, 640–649 (2009). doi:10.1088/0004-637X/691/1/640
F.J. Rogers, F.J. Swenson, C.A. Iglesias, OPAL equation-of-state tables for astrophysical applications. ApJ 456, 902 (1996). doi:10.1086/176705
R.F. Stein, Å. Nordlund, D. Georgoviani, D. Benson, W. Schaffenberger, Supergranulation-scale convection simulations, in Solar-Stellar Dynamos as Revealed by Helio- and Asteroseismology: GONG 2008/SOHO 21. Astronomical Society of the Pacific Conference Series, vol. 416, ed. by M. Dikpati, T. Arentoft, I. González Hernández, C. Lindsey, F. Hill (2009), p. 421
A. Vögler, S. Shelyag, M. Schüssler, F. Cattaneo, T. Emonet, T. Linde, Simulations of magneto-convection in the solar photosphere. Equations, methods, and results of the MURaM code. A&A 429, 335–351 (2005). doi:10.1051/0004-6361:20041507
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2015 Springer Japan
About this chapter
Cite this chapter
Hotta, H. (2015). Basic Equations and Development of Numerical Code. In: Thermal Convection, Magnetic Field, and Differential Rotation in Solar-type Stars. Springer Theses. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55399-1_2
Download citation
DOI: https://doi.org/10.1007/978-4-431-55399-1_2
Published:
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-55398-4
Online ISBN: 978-4-431-55399-1
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)