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    Code development of three-dimensional general relativistic hydrodynamics with AMR (adaptive-mesh refinement) and results from special and general relativistic hydrodynamics
    (KLUWER ACADEMIC PUBL, 2004) Donmez, O
    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.
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    Numerical simulation of rotating accretion disk around the Schwarzschild black hole using GRH code
    (ELSEVIER SCIENCE INC, 2006) Donmez, O
    The 2D time dependent solution of thin accretion disk in a close binary system have been presented on the equatorial plane around the Schwarzschild black hole. To do that, the special part of the general relativistic hydrodynamical (GRH) equations are solved using high resolution shock capturing (HRSC) schemes. The spiral shock waves on the accretion disk are modeled using perfect fluid equation of state with adiabatic indices gamma = 1.05, 1.2 and 5/3. The results show that the spiral shock waves are created for gammas except the case gamma = 5/3. These results are consistent with the results from Newtonian hydrodynamic code except those which are close to black hole. Newtonian approximation does not give good solution when the matter is close to the black hole. Our simulations illustrate that the spiral shock waves are created close to black hole and the location of inner radius of spiral shock wave is around 6M and it depends on the specific heat rates. We also find that the smaller gamma is the more tightly packed in the spiral winds. (c) 2005 Elsevier Inc. All rights reserved.