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Numerical Hydrodynamics and Magnetohydrodynamics in General Relativity.

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This review details numerical methods for general relativistic hydrodynamics and magneto-hydrodynamics (MHD). It covers advanced techniques for astrophysical simulations, including black hole accretion and neutron star evolution.

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Area of Science:

  • Astrophysical simulations
  • Numerical relativity
  • Computational astrophysics

Background:

  • This article is the third version of a review on numerical hydrodynamics and magneto-hydrodynamics (MHD) in general relativity.
  • Significant updates include comprehensive coverage of general-relativistic MHD, reflecting recent advancements in the field.

Purpose of the Study:

  • To provide an updated overview of numerical methods in general relativistic hydrodynamics and MHD.
  • To detail recent advances in astrophysical simulations within strong gravitational fields.
  • To discuss numerical approaches for solving hyperbolic systems of equations.

Main Methods:

  • Presentation of conservative and hyperbolic formulations of hydrodynamics and MHD equations.
  • Discussion of numerical approaches, including linearized Riemann solvers.
  • Focus on multidimensional simulation studies.

Main Results:

  • Detailed coverage of general-relativistic MHD for the first time.
  • Enlarged discussion of astrophysical simulations in general-relativistic hydrodynamics.
  • Summary of simulations for gravitational collapse, black-hole accretion, and neutron-star evolutions.

Conclusions:

  • The review highlights numerical challenges in simulating astrophysical phenomena in strong gravity.
  • It emphasizes the chronological development of numerical methods and equation formulations.
  • The focus on multidimensional studies provides a contemporary perspective on the field.