Assessment of the MUSTA approach for numerical relativistic hydrodynamics

¹ Laboratory for Scientific Computing, Department of Physics, Cavendish Laboratory, J J Thomson Avenue, Cambridge, CB3 0HE, UK
e-mail: pmb39@cam.ac.uk; nn10005@cam.ac.uk
² Department of Mathematical Sciences, Rensselaer Polytechnic Institute, NY 12180 Troy, USA
e-mail: henshw@rpi.edu

Received: 20 October 2014
Accepted: 25 December 2014

Abstract

Aims. We evaluate some approximations for solving the equations of special relativistic hydrodynamics within complex geometries. In particular, we assess the following schemes: the Generalized FORCE (GFORCE) and MUlti STAge (MUSTA) approaches which are used as the basis for a second-order-accurate Slope-LImited-Centred (SLIC) method. These do not require detailed knowledge of the characteristic structure of the system, but have the potential to be nearly as accurate as more expensive schemes which do require this knowledge.

Methods. In order to treat complex geometries, we use multiple overlapping grids which allow the capturing of complex geometries while retaining the efficiencies associated with structured grids.

Results. The schemes are evaluated using a suite of one dimensional problems some of which have known exact solutions, and it is shown that the schemes can be used at CFL numbers close to the theoretical stability limit. We compare the effects of the MUSTA approach when applied to two different schemes. The scheme is further validated on a number of problems involving complex geometries with overlapping grids.