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


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: (P. A. Gremaud), (Y. Sun)

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