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 numericalrelativity simulations at smaller computational costs and at considerably larger spatial resolutions. We present here a new fluxconservative 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 shocktube tests.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 November 2008
 DOI:
 10.1088/02649381/25/22/225007
 arXiv:
 arXiv:0811.0938
 Bibcode:
 2008CQGra..25v5007K
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 19 pages, 9 figures