An improved formulation of the relativistic hydrodynamics equations in 2D Cartesian coordinates
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.
- Publication:
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Classical and Quantum Gravity
- Pub Date:
- November 2008
- DOI:
- 10.1088/0264-9381/25/22/225007
- arXiv:
- arXiv:0811.0938
- Bibcode:
- 2008CQGra..25v5007K
- Keywords:
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- General Relativity and Quantum Cosmology
- E-Print:
- 19 pages, 9 figures