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Volume 28, Issue 3
Mathematical Aspects Relative to the Fluid Statics of a Self-Gravitating Perfect-Gas Isothermal Sphere

Pierluigi Amodio, Domenico Giordano, Felice Iavernaro, Arcangelo Labianca, Monica Lazzo, Francesca Mazzia & Lorenzo Pisani

DOI: 10.4208/cicp.OA-2019-0203

Commun. Comput. Phys., 28 (2020), pp. 1085-1104.

Published online: 2020-07

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  • Abstract

In the present paper we analyze and discuss some mathematical aspects of the fluid-static configurations of a self-gravitating perfect gas enclosed in a spherical solid shell. The mathematical model we consider is based on the well-known Lane-Emden equation, albeit under boundary conditions that differ from those usually assumed in the astrophysical literature. The existence of multiple solutions requires particular attention in devising appropriate numerical schemes apt to deal with and catch the solution multiplicity as efficiently and accurately as possible. In sequence, we describe some analytical properties of the model, the two algorithms used to obtain numerical solutions, and the numerical results for two selected cases.

  • Keywords

Self-gravitating gas, Lane-Emden equation, multiple solutions.

  • AMS Subject Headings

76N10, 34B08, 65L10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-28-1085, author = {Amodio , PierluigiGiordano , DomenicoIavernaro , FeliceLabianca , ArcangeloLazzo , MonicaMazzia , Francesca and Pisani , Lorenzo}, title = {Mathematical Aspects Relative to the Fluid Statics of a Self-Gravitating Perfect-Gas Isothermal Sphere}, journal = {Communications in Computational Physics}, year = {2020}, volume = {28}, number = {3}, pages = {1085--1104}, abstract = {

In the present paper we analyze and discuss some mathematical aspects of the fluid-static configurations of a self-gravitating perfect gas enclosed in a spherical solid shell. The mathematical model we consider is based on the well-known Lane-Emden equation, albeit under boundary conditions that differ from those usually assumed in the astrophysical literature. The existence of multiple solutions requires particular attention in devising appropriate numerical schemes apt to deal with and catch the solution multiplicity as efficiently and accurately as possible. In sequence, we describe some analytical properties of the model, the two algorithms used to obtain numerical solutions, and the numerical results for two selected cases.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2019-0203}, url = {http://global-sci.org/intro/article_detail/cicp/17676.html} }
TY - JOUR T1 - Mathematical Aspects Relative to the Fluid Statics of a Self-Gravitating Perfect-Gas Isothermal Sphere AU - Amodio , Pierluigi AU - Giordano , Domenico AU - Iavernaro , Felice AU - Labianca , Arcangelo AU - Lazzo , Monica AU - Mazzia , Francesca AU - Pisani , Lorenzo JO - Communications in Computational Physics VL - 3 SP - 1085 EP - 1104 PY - 2020 DA - 2020/07 SN - 28 DO - http://doi.org/10.4208/cicp.OA-2019-0203 UR - https://global-sci.org/intro/article_detail/cicp/17676.html KW - Self-gravitating gas, Lane-Emden equation, multiple solutions. AB -

In the present paper we analyze and discuss some mathematical aspects of the fluid-static configurations of a self-gravitating perfect gas enclosed in a spherical solid shell. The mathematical model we consider is based on the well-known Lane-Emden equation, albeit under boundary conditions that differ from those usually assumed in the astrophysical literature. The existence of multiple solutions requires particular attention in devising appropriate numerical schemes apt to deal with and catch the solution multiplicity as efficiently and accurately as possible. In sequence, we describe some analytical properties of the model, the two algorithms used to obtain numerical solutions, and the numerical results for two selected cases.

Pierluigi Amodio, Domenico Giordano, Felice Iavernaro, Arcangelo Labianca, Monica Lazzo, Francesca Mazzia & Lorenzo Pisani. (2020). Mathematical Aspects Relative to the Fluid Statics of a Self-Gravitating Perfect-Gas Isothermal Sphere. Communications in Computational Physics. 28 (3). 1085-1104. doi:10.4208/cicp.OA-2019-0203
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