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A recent paper by Lucas-Serrano et al. indicates that a high-resolutioncentral (HRC) scheme is robust enough to yield accurate hydrodynamicalsimulations of special relativistic flows in the presence of ultrarelativisticspeeds and strong shock waves. In this paper we apply this scheme in fullgeneral relativity (involving {\it dynamical} spacetimes), and assess itssuitability by performing test simulations for oscillations of rapidly rotatingneutron stars and merger of binary neutron stars. It is demonstrated that thisHRC scheme can yield results as accurate as those by the so-calledhigh-resolution shock-capturing (HRSC) schemes based upon Riemann solvers.Furthermore, the adopted HRC scheme has increased computational efficiency asit avoids the costly solution of Riemann problems and has practical advantagesin the modeling of neutron star spacetimes. Namely, it allows simulations withstiff equations of state by successfully dealing with very low-densityunphysical atmospheres. These facts not only suggest that such a HRC scheme maybe a desirable tool for hydrodynamical simulations in general relativity, butalso open the possibility to perform accurate magnetohydrodynamical simulationsin curved dynamic spacetimes.Comment: 4 pages, to be published in Phys. Rev. D (brief report

Robustness of a high-resolution central scheme for hydrodynamic simulations in full general relativity