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G. A. Richardson (NRC / MSFC), T. J. Chung (University of Alabama - Huntsville)
We present our method for solving the equations associated with general relativistic magneto-hydrodynamics. Relativistic effects become pronounced in such cases as jet formation from black hole magnetized accretion disks. Non-ideal flows are present in accretion disks where diffusion plays an important role in heat and energy transport. Our concern in this paper is to re-examine existing numerical simulations tools as to the accuracy and efficiency of computations and introduce a new approach known as the flowfield-dependent variation (FDV) method. The main feature of the FDV method consists of accommodating discontinuities of shock waves and high gradients of flow variables such as occur in turbulence and unstable motions. In this paper, the physics involved in the solution of relativistic hydrodynamics and solution strategies of the FDV theory are elaborated. Some preliminary Kerr metric magneto-hydrodynamic results will also be discussed. The general relativistic astrophysical flow and shock solver (GRAFSS) will be introduced. GRAFFS is a multi-dimensional finite element code based on the FDV theory capable of solving complex geometries. Example problems in computational relativistic astrophysics will be demonstrated to show the feasibility of GRAFSS when modeling discontinuities and regions with extreme gravitational fields.
This work has been supported in part by the National Research Council fellowship program.
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Bulletin of the American Astronomical Society, 34
© 2002. The American Astronomical Soceity.