A consistent numerical scheme for self‐gravitating fluid dynamics. Issue 1 (5th March 2012)

• Record Type: Journal Article
• Authors: Colombeau, M.
• Is Part Of: Numerical methods for partial differential equations. Volume 29:Issue 1(2013:Jan.)
• Page Start: 79
• Page End: 101
• Publication Date: 2012-03-05
• Subjects: Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.21700
• Languages: English
• ISSNs: 0749-159X

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>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 <italic>L</italic>^{<italic>∞</italic>} functions in velocity and <italic>L</italic>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</p> </abstract>