An algorithm for computing the 2D structure of fast rotating stars
| Autor: | Bertrand Putigny, M. Rieutord, Francisco Espinosa Lara |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Physics
Numerical Analysis Chebyshev polynomials Partial differential equation Physics and Astronomy (miscellaneous) Discretization 010308 nuclear & particles physics Applied Mathematics Spherical harmonics FOS: Physical sciences Solver 01 natural sciences Computer Science Applications Gravitation Computational Mathematics symbols.namesake Nonlinear system Astrophysics - Solar and Stellar Astrophysics Modeling and Simulation 0103 physical sciences Jacobian matrix and determinant symbols 010303 astronomy & astrophysics Algorithm Solar and Stellar Astrophysics (astro-ph.SR) |
| Popis: | Stars may be understood as self-gravitating masses of a compressible fluid whose radiative cooling is compensated by nuclear reactions or gravitational contraction. The understanding of their time evolution requires the use of detailed models that account for a complex microphysics including that of opacities, equation of state and nuclear reactions. The present stellar models are essentially one-dimensional, namely spherically symmetric. However, the interpretation of recent data like the surface abundances of elements or the distribution of internal rotation have reached the limits of validity of one-dimensional models because of their very simplified representation of large-scale fluid flows. In this article, we describe the ESTER code, which is the first code able to compute in a consistent way a two-dimensional model of a fast rotating star including its large-scale flows. Compared to classical 1D stellar evolution codes, many numerical innovations have been introduced to deal with this complex problem. First, the spectral discretization based on spherical harmonics and Chebyshev polynomials is used to represent the 2D axisymmetric fields. A nonlinear mapping maps the spheroidal star and allows a smooth spectral representation of the fields. The properties of Picard and Newton iterations for solving the nonlinear partial differential equations of the problem are discussed. It turns out that the Picard scheme is efficient on the computation of the simple polytropic stars, but Newton algorithm is unsurpassed when stellar models include complex microphysics. Finally, we discuss the numerical efficiency of our solver of Newton iterations. This linear solver combines the iterative Conjugate Gradient Squared algorithm together with an LU-factorization serving as a preconditionner of the Jacobian matrix. 40 pages, 12 figures, accepted in J. Comput. Physics |
| Databáze: | OpenAIRE |
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