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A consistent numerical scheme for self‐gravitating fluid dynamics
Author(s) -
Colombeau M.
Publication year - 2013
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21700
Subject(s) - consistency (knowledge bases) , mathematics , gravitational field , gravitation , scheme (mathematics) , gravitational force , dark matter , numerical analysis , cosmology , partial differential equation , field (mathematics) , classical mechanics , mathematical analysis , mathematical physics , physics , pure mathematics , geometry , astrophysics
Abstract In this article, we present a numerical scheme for the 3‐D system of self‐gravitating fluid dynamics in the collisional case as well as in the non‐collisional case. Consistency in the sense of distributions is proved in 1‐D and in absence of pressure. In the other cases consistency is proved under the numerical assumptions of boundedness of the velocity field in the CFL condition and of boundedness of the gradient of the gravitation potential. In 2‐D and 3‐D, concentrations of matter in strings and points can cause a theoretical difficulty in the pressureless case although one observes that the scheme still works. The initial data are L ∞ functions in velocity and L 1 functions in density. Applications are given to numerical simulations of the role of dark matter and gravitational collapse in cosmology as well as Jeans theory. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013