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Riemann solvers in relativistic astrophysics. (English) Zbl 0945.76060
Summary: We review high resolution shock capturing methods (HRSC) in the field of relativistic hydrodynamics with special emphasis on Riemann solvers. HRSC techniques achieve highly accurate numerical approximations (formally second-order or better) in smooth regions of the flow, and capture the motion of unresolved steep gradients without creating spurious oscillations. One objective of our contribution is to show how these techniques have been extended to relativistic hydrodynamics, making it possible to explore some challenging astrophysical scenarios. We review recent literature concerning the main properties of different special relativistic Riemann solvers, and discuss several one- and two-dimensional test problems which are commonly used to evaluate the performance of numerical methods in relativistic hydrodynamics. Finally, we illustrate the use of HRSC methods in several applications in special and general relativistic hydrodynamics.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
85-08 Computational methods for problems pertaining to astronomy and astrophysics
76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
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