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An improved formulation of the relativistic hydrodynamics equations in 2D Cartesian coordinates

MPS-Authors

Kellerman,  Thorsten
MPI for Gravitational Physics, Max Planck Society;

Baiotti,  Luca
MPI for Gravitational Physics, Max Planck Society;

Giacomazzo,  Bruno
MPI for Gravitational Physics, Max Planck Society;

Rezzolla,  Luciano
Astrophysical Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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cqg8_22_225007.pdf
(Publisher version), 473KB

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Citation

Kellerman, T., Baiotti, L., Giacomazzo, B., & Rezzolla, L. (2008). An improved formulation of the relativistic hydrodynamics equations in 2D Cartesian coordinates. Classical and Quantum Gravity, 25(22): 225007. doi:10.1088/0264-9381/25/22/225007.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-138B-B
Abstract
A number of astrophysical scenarios possess and preserve an overall cylindrical symmetry when also undergoing a catastrophic and nonlinear evolution. Exploiting such a symmetry, these processes can be studied through numerical-relativity simulations at smaller computational costs and at considerably larger spatial resolutions. We present here a new flux-conservative formulation of the relativistic hydrodynamics equations in cylindrical coordinates. By rearranging those terms in the equations which are the sources of the largest numerical errors, the new formulation yields a global truncation error, which is one or more orders of magnitude smaller than those of alternative and commonly used formulations. We illustrate this through a series of numerical tests involving the evolution of oscillating spherical and rotating stars, as well as shock-tube tests.