Commun. Comput. Phys., 11 (2012), pp. 114-146.


An Adaptive Moving Mesh Method for Two-Dimensional Relativistic Hydrodynamics

Peng He 1, Huazhong Tang 1*

1 HEDPS, CAPT and LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China.

Received 29 October 2010; Accepted (in revised version) 18 March 2011
Available online 5 September 2011
doi:10.4208/cicp.291010.180311a

Abstract

This paper extends the adaptive moving mesh method developed by Tang and Tang [36] to two-dimensional (2D) relativistic hydrodynamic (RHD) equations. The algorithm consists of two "independent" parts: the time evolution of the RHD equations and the (static) mesh iteration redistribution. In the first part, the RHD equations are discretized by using a high resolution finite volume scheme on the fixed but nonuniform meshes without the full characteristic decomposition of the governing equations. The second part is an iterative procedure. In each iteration, the mesh points are first redistributed, and then the cell averages of the conservative variables are remapped onto the new mesh in a conservative way. Several numerical examples are given to demonstrate the accuracy and effectiveness of the proposed method.

AMS subject classifications: 35L65, 65M50, 74S10, 76L05, 76N15, 76Y05

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Key words: Adaptive moving mesh method, finite volume method, conservative interpolation, relativistic hydrodynamics.

*Corresponding author.
Email: hepengpku@gmail.com (P. He), hztang@math.pku.edu.cn (H. Z. Tang)
 

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