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An adaptive moving mesh method for two-dimensional relativistic hydrodynamics. (English) Zbl 1373.76354
Summary: This paper extends the adaptive moving mesh method developed by H. Tang and T. Tang [SIAM J. Numer. Anal. 41, No. 2, 487–515 (2003; Zbl 1052.65079)] 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.

MSC:
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
76M12 Finite volume methods applied to problems in fluid mechanics
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
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