2019/03/10 by Domenico Giordano, D. Giordano, Pierluigi Amodio +5
Mathematics · Physics and Astronomy · #Boundary value problem #Classical mechanics #Cosmology and Gravitation Theories #Field (mathematics) #Gravitation #Gravitational field #Isothermal process #Mathematics #Mechanics #Perfect fluid #Physics #Pulsars and Gravitational Waves Research #Statics #Statistical Mechanics and Entropy #Statistical physics #Thermodynamics #physics.flu-dyn
paper · pdf · doi:10.1016/j.euromechflu.2019.05.013
published as European Journal of Mechanics B / Fluids, 78, pp. 62-87, 2019 · 32 pages, 26 figures
arxiv created 2019/03/10 · openalex publication_date 2019/06/03 · arxiv updated 2019/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We open the paper with introductory considerations describing the motivations of our long-term research plan targeting gravitomagnetism, illustrating the fluid-dynamics numerical test case selected for that purpose, that is, a perfect-gas sphere contained in a solid shell located in empty space sufficiently away from other masses, and defining the main objective of this study: the determination of the gravitofluid-static field required as initial field (t=0) in forthcoming fluid-dynamics calculations. The determination of the gravitofluid-static field requires the solution of the isothermal-sphere Lane-Emden equation. We do not follow the habitual approach of the literature based on the prescription of the central density as boundary condition; we impose the gravitational field at the solid-shell internal wall. As the discourse develops, we point out differences and similarities between the literature's and our approach. We show that the nondimensional formulation of the problem hinges on a unique physical characteristic number that we call gravitational number because it gauges the self-gravity effects on the gas' fluid statics. We illustrate and discuss numerical results; some peculiarities, such as gravitational-number upper bound and multiple solutions, lead us to investigate the thermodynamics of the physical system, particularly entropy and energy, and preliminarily explore whether or not thermodynamic-stability reasons could provide justification for either selection or exclusion of multiple solutions. We close the paper with a summary of the present study in which we draw conclusions and describe future work.