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Title: Radially symmetric solutions of the ultra-relativistic Euler equations in several space dimensions
Author(s): Kunik, Matthias
Kolb, Adrain
Müller, Siegfried
Thein, Ferdinand
Issue Date: 2024-02-22
Type: Preprint
Language: English
Publisher: Otto von Guericke University Library, Magdeburg, Germany
URN: urn:nbn:de:gbv:ma9:1-1981185920-1171962
Subjects: Euler
space dimensions
Abstract: The ultra-relativistic Euler equations for an ideal gas are described in terms of the pressure, the spatial part of the dimension- less four-velocity and the particle density. Radially symmetric solutions of these equations are studied in two and three space dimensions. Of particular interest in the solutions are the formation of shock waves and a pressure blow up. For the investigation of these phenomena we develop a one-dimensional scheme using radial symmetry and integral conservation laws. We compare the numerical results with solutions of multi-dimensional high-order numerical schemes for general initial data in two space dimensions. The presented test cases and results may serve as interesting benchmark tests for multi-dimensional solvers.
Open Access: Open access publication
License: (CC BY-SA 4.0) Creative Commons Attribution ShareAlike 4.0(CC BY-SA 4.0) Creative Commons Attribution ShareAlike 4.0
Appears in Collections:Fakultät für Mathematik (OA)

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