| Abstract: | In this paper, the general procedure to solve the general relativistic hydrodynamical (GRH) equations with adaptive-mesh refinement
(AMR) is presented. In order to achieve, the GRH equations are written in the conservation form to exploit their hyperbolic
character. The numerical solutions of GRH equations are obtained by high resolution shock Capturing schemes (HRSC), specifically
designed to solve nonlinear hyperbolic systems of conservation laws. These schemes depend on the characteristic information
of the system. The Marquina fluxes with MUSCL left and right states are used to solve GRH equations. First, different test
problems with uniform and AMR grids on the special relativistic hydrodynamics equations are carried out to verify the second-order
convergence of the code in one, two and three dimensions. Results from uniform and AMR grid are compared. It is found that
adaptive grid does a better job when the number of resolution is increased. Second, the GRH equations are tested using two
different test problems which are Geodesic flow and Circular motion of particle In order to do this, the flux part of GRH
equations is coupled with source part using Strang splitting. The coupling of the GRH equations is carried out in a treatment
which gives second order accurate solutions in space and time.
This revised version was published online in July 2006 with corrections to the Cover Date. |
