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An adaptive moving mesh method for two-dimensional relativistic magnetohydrodynamics. (English) Zbl 1365.76337
Summary: This paper develops an adaptive moving mesh method for two-dimensional ideal relativistic magnetohydrodynamical (RMHD) equations that utilizes the initial reconstruction of the primitive variables in the logical domain and the projection technique for the solenoidal constraint of the magnetic field. The method consists of two “independent” parts: the time evolution of the RMHD equations and the mesh iteration redistribution. In the first part, the RMHD equations are solved on a fixed quadrangular mesh by using a high-resolution shock-capturing scheme. 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 experiments are carried out to demonstrate the accuracy and effectiveness of the proposed method.

76W05 Magnetohydrodynamics and electrohydrodynamics
76M12 Finite volume methods applied to problems in fluid mechanics
65N08 Finite volume methods for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
Full Text: DOI
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