6533b824fe1ef96bd127fe9b

RESEARCH PRODUCT

An introduction to relativistic hydrodynamics

José A. Font

subject

PhysicsHistoryConservation lawGeneral relativitySpace timeEulerian pathComputer Science ApplicationsEducationMagnetic fieldsymbols.namesakeRiemann hypothesisClassical mechanicsInviscid flowsymbolsMagnetohydrodynamics

description

We review formulations of the equations of (inviscid) general relativistic hydrodynamics and (ideal) magnetohydrodynamics, along with methods for their numerical solution. Both systems can be cast as first-order, hyperbolic systems of conservation laws, following the explicit choice of an Eulerian observer and suitable fluid and magnetic field variables. During the last fifteen years, the so-called (upwind) high-resolution shock-capturing schemes based on Riemann solvers have been successfully extended from classical to relativistic fluid dynamics, both special and general. Nowadays, general relativistic hydrodynamical simulations in relativistic astrophysics are routinely performed, particularly within the test-fluid approximation but also for dynamical spacetimes. While such advances also hold true in the case of the MHD equations, the astrophysical applications investigated so far are still limited, yet the field is bound to witness major developments in the near future. The article also presents a brief overview of numerical techniques, providing state-of-the-art examples of their applicability to general relativistic fluids and magneto-fluids in characteristic scenarios of relativistic astrophysics.

https://doi.org/10.1088/1742-6596/91/1/012002