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Riemann solvers in general relativistic hydrodynamics. (English) Zbl 1064.76567
Toro, E. F. (ed.), Godunov methods. Theory and applications. International conference, Oxford, GB, October 1999. New York, NY: Kluwer Academic/ Plenum Publishers (ISBN 0-306-46601-5). 485-496 (2001).
Summary: Our contribution concerns with the numerical solution of the 3D general relativistic hydrodynamical system of equations within the framework of the $$\{3+1\}$$ formalism. We summarize the theoretical ingredients which are necessary in order to build up a numerical scheme based on the solution of local Riemann problems. Hence, the full spectral decomposition of the Jacobian matrices of the system, i.e., the eigenvalues and the right and left eigenvectors, is explicitly shown. An alternative approach consists in using any of the special relativistic Riemann solvers recently developed for describing the evolution of special relativistic flows. Our proposal relies on a local change of coordinates in terms of which the space-time metric is locally Minkowskian and permits an accurate description of numerical general relativistic hydrodynamics.
For the entire collection see [Zbl 0978.00036].

##### MSC:
 76M12 Finite volume methods applied to problems in fluid mechanics 65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems 76Y05 Quantum hydrodynamics and relativistic hydrodynamics 83-08 Computational methods for problems pertaining to relativity and gravitational theory