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

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##### Fulltext (public)

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.