Commun. Comput. Phys., 16 (2014), pp. 348-364.


Numerical Study of Singularity Formation in Relativistic Euler Flows

Pierre A. Gremaud 1, Yi Sun 2*

1 Department of Mathematics, North Carolina State University, Raleigh, NC, 27695, USA.
2 Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA.

Received 22 December 2012; Accepted (in revised version) 30 January 2014
Available online 17 April 2014
doi:10.4208/cicp.221212.300114a

Abstract

The formation of singularities in relativistic flows is not well understood. Smooth solutions to the relativistic Euler equations are known to have a finite life-span; the possible breakdown mechanisms are shock formation, violation of the sub-luminal conditions and mass concentration. We propose a new hybrid Glimm/central-upwind scheme for relativistic flows. The scheme is used to numerically investigate, for a family of problems, which of the above mechanisms is involved.

AMS subject classifications: 35L67, 65M08, 65M25, 76Y05, 83C05, 83C75

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Key words: Relativistic Euler equations, singularity formation, Glimm scheme, central-upwind scheme, hybrid method.

*Corresponding author.
Email: gremaud@ncsu.edu (P. A. Gremaud), yisun@math.sc.edu (Y. Sun)
 

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