Local characteristic algorithms for relativistic hydrodynamics

Details Local characteristic algorithms for relativistic hydrodynamics Local characteristic algorithms for relativistic hydrodynamics

2002-03-22

arxiv.org/abs/astro-ph/0203404v1

Lect.NotesPhys.604:327-348,2002

Astronomy and Astrophysics

Astrophysics

20 pages, 4 figures, To appear in the proceedings of the workshop "The conformal structure of space-time", J. Frauendiener, H.

Scientific paper

Numerical schemes for the general relativistic hydrodynamic equations are discussed. The use of conservative algorithms based upon the characteristic structure of those equations, developed during the last decade building on ideas first applied in Newtonian hydrodynamics, provides a robust methodology to obtain stable and accurate solutions even in the presence of discontinuities. The knowledge of the wave structure of the above system is essential in the construction of the so-called linearized Riemann solvers, a class of numerical schemes specifically designed to solve nonlinear hyperbolic systems of conservation laws. In the last part of the review some astrophysical applications of such schemes, using the coupled system of the (characteristic) Einstein and hydrodynamic equations, are also briefly presented.

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