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arXiv · 0811.0938

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

Thorsten Kellermann·Luca Baiotti·Bruno Giacomazzo·Luciano Rezzolla
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Abstract

A number of astrophysical scenarios possess and preserve an overall cylindrical symmetry also when 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 here present 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.

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Thorsten Kellermann, Luca Baiotti, Bruno Giacomazzo, Luciano Rezzolla. 2008-12-02. An improved formulation of the relativistic hydrodynamics equations in 2D Cartesian coordinates. https://doi.org/10.1088/0264-9381%2F25%2F22%2F225007

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