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João Pedro Marques Mário João Monteiro

João Pedro Marques Mário João Monteiro. CESAM2K. CoRoT/ESTA - Aarhus Workshop. Numerics. Solution of the stellar structure eqs. by collocation method based on piecewise polynomial approximations projected on their B-spline basis Stable and robust calculations

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João Pedro Marques Mário João Monteiro

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  1. João Pedro Marques Mário João Monteiro CESAM2K CoRoT/ESTA - Aarhus Workshop

  2. Numerics • Solution of the stellar structure eqs. by collocation method based on piecewise polynomial approximations projected on their B-spline basis • Stable and robust calculations • Restitution of the solution not only at grid points • Automatic mesh refinement

  3. Numerics • Precise restoration of the atmosphere • Modular in design • Evolution of the chemical composition: • Without diffusion: implicit Runge-Kutta scheme • With diffusion: solution of the diffusion eq. using the Galerkin method

  4. Equation of state • OPAL 2001 EoS tables used with the OPAL interpolation scheme • Other EoS available: • EFF • CEFF • MHD

  5. Opacity • OPAL 1996 + Alexander & Ferguson 1994: • Houdek9 interpolation • Interpolation by Lagrange Polynomials for log T6 and log R, quadratic interpolation for X and Z • Other opacities: • Interpolation of the tables of Livermore 1991

  6. Energy generation rate • NACRE compilation (other compilations available, e. g. Caughlan and Fowler 1988). • Several networks available (PP+CNO+3a). Examples: • PP+CNO chains with 2H and 7Be in equilibrium • PP+CNO without any element in equilibrium • PP+CNO+3a

  7. Convection • Böhm-Vitense MLT taking into account the optical thickness of the bubble. l= aHP • CM (1991) with l = aHP • CGM (1996)

  8. Atmosphere • T(t) relation based on the grey Hopf atmospheric law. Connection with the envelope at t=10. • Other T(t) relations available: • Eddington law • T(t) for the Sun calculated with Atlas 9 of Kurucz (for Teff=5750, 5777 K) • T(t) calculated with Atlas 12 of Kurucz (for [Fe/H=0, -0.2, -0.5, -1.0) • Single shell

  9. Code available upon request at http://www.obs-nice.fr/morel/CESAM_PROTECT/CESAM.html Package contains a detailed description of the code (in french), as well as a user's guide Description in english: Morel 1997, A&AS, 124, 597 Detailed description of the code

  10. CESAM2K V2 • Many mesh points added around the CZ/RZ limits to refine the profile of the Brunt-Väissälä frequency • Possibility to use either the radiative or the adiabatic gradient on the overshoot zones • Diffusion of the angular momentum

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