Issue |
A&A
Volume 626, June 2019
|
|
---|---|---|
Article Number | A108 | |
Number of page(s) | 11 | |
Section | Numerical methods and codes | |
DOI | https://doi.org/10.1051/0004-6361/201935669 | |
Published online | 21 June 2019 |
Interpolation of equation-of-state data
1
Sternberg Astronomical Institute, M.V. Lomonosov Moscow State University, 13, Universitetskij pr., 119234 Moscow, Russia
e-mail: avo@sai.msu.ru
2
Department of Physics and Astronomy, University of Southern California, Los Angeles, CA 90089, USA
Received:
12
April
2019
Accepted:
26
April
2019
Aims. We use Hermite splines to interpolate pressure and its derivatives simultaneously, thereby preserving mathematical relations between the derivatives. The method therefore guarantees that thermodynamic identities are obeyed even between mesh points. In addition, our method enables an estimation of the precision of the interpolation by comparing the Hermite-spline results with those of frequent cubic (B-) spline interpolation.
Methods. We have interpolated pressure as a function of temperature and density with quintic Hermite 2D-splines. The Hermite interpolation requires knowledge of pressure and its first and second derivatives at every mesh point. To obtain the partial derivatives at the mesh points, we used tabulated values if given or else thermodynamic equalities, or, if not available, values obtained by differentiating B-splines.
Results. The results were obtained with the grid of the SAHA-S equation-of-state (EOS) tables. The maximum lgP difference lies in the range from 10−9 to 10−4, and Γ1 difference varies from 10−9 to 10−3. Specifically, for the points of a solar model, the maximum differences are one order of magnitude smaller than the aforementioned values. The poorest precision is found in the dissociation and ionization regions, occurring at T ∼ 1.5 × 103−105 K. The best precision is achieved at higher temperatures, T > 105 K. To discuss the significance of the interpolation errors we compare them with the corresponding difference between two different equation-of-state formalisms, SAHA-S and OPAL 2005. We find that the interpolation errors of the pressure are a few orders of magnitude less than the differences from between the physical formalisms, which is particularly true for the solar-model points.
Key words: equation of state / methods: numerical / Sun: evolution / Sun: interior / stars: evolution / stars: interiors
© ESO 2019
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.