Numerical Hydrodynamics in General Relativity

Numerical Hydrodynamics in General Relativity

The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced numerical methods. A representative sample of available numerical schemes is discussed and particular emphasis is paid to solution proc...

Numerical Hydrodynamics and Magnetohydrodynamics in General Relativity

This article presents a comprehensive overview of numerical hydrodynamics and magneto-hydrodynamics (MHD) in general relativity. Some significant additions have been incorporated with respect to the previous two versions of this review (2000, 2003), most notably the coverage of general-relativistic MHD, a field in which remarkable activity and progress has occurred in the last few years. Corres...

Numerical Hydrodynamics in Special Relativity

This review is concerned with a discussion of numerical methods for the solution of the equations of special relativistic hydrodynamics (SRHD). Particular emphasis is put on a comprehensive review of the application of high-resolution shock-capturing methods in SRHD. Results obtained with different numerical SRHD methods are compared, and two astrophysical applications of SRHD flows are discuss...

Numerical Problems in General Relativity

The construction of gravitational wave observatories is one of the greatest scientific efforts of our time. As a result, there is presently a strong need to numerically simulate the emission of gravitation radiation from massive astronomical events such as black hole collisions. This entails the numerical solution of the Einstein field equations. We briefly describe the field equations in their...

Relativistic Hydrodynamics and other topics in Numerical Relativity