Volume 428, Number 2, December III 2004
|Page(s)||703 - 715|
|Published online||26 November 2004|
Assessment of a high-resolution central scheme for the solution of the relativistic hydrodynamics equations
Departamento de Astronomía y Astrofísica, Universidad de Valencia, Edificio de Investigación, Dr. Moliner 50, 46100 Burjassot (Valencia), Spain e-mail: firstname.lastname@example.org
Accepted: 22 July 2004
We assess the suitability of a recent high-resolution central scheme developed by [CITE] for the solution of the relativistic hydrodynamic equations. The novelty of this approach relies on the absence of Riemann solvers in the solution procedure. The computations we present are performed in one and two spatial dimensions in Minkowski spacetime. Standard numerical experiments such as shock tubes and the relativistic flat-faced step test are performed. As an astrophysical application the article includes two-dimensional simulations of the propagation of relativistic jets using both Cartesian and cylindrical coordinates. The simulations reported clearly show the capabilities of the numerical scheme of yielding satisfactory results, with an accuracy comparable to that obtained by the so-called high-resolution shock-capturing schemes based upon Riemann solvers (Godunov-type schemes), even well inside the ultrarelativistic regime. Such a central scheme can be straightforwardly applied to hyperbolic systems of conservation laws for which the characteristic structure is not explicitly known, or in cases where a numerical computation of the exact solution of the Riemann problem is prohibitively expensive. Finally, we present comparisons with results obtained using various Godunov-type schemes as well as with those obtained using other high-resolution central schemes which have recently been reported in the literature.
Key words: hydrodynamics / methods: numerical / relativity / shock waves
© ESO, 2004
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.