Finite Element Analysis for General Relativistic Flow Environments

Statistics – Computation

Scientific paper

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Scientific paper

We present our finite element methodology for numerically solving the governing equations for general relativistic environments. Our motivation for the development of such a method is to study the environment around a rotating black hole, specifically the dynamics of the accretion disk and the associated formation of relativistic jets. The numerical technique we have developed is versatile enough to perform simulations ranging from relativistic shock capturing in magnetohydrodynamics to Poisson solvers for mapping fields. This numerical technique is unique in its ability to detect small variations in the physical parameters related to the flow-field or the magnetic field. Since this information is obtained during the computations, it can be used for adaptive mesh refinement, necessary variations in the PDE solver, the detection of numerical instabilities and potentially for the detection of turbulence. This direct link between the variations in the physical parameters and the numerical parameters helps to increase the accuracy and the stability of the system. While we have developed this method for use in finite element analysis, it is also possible to adapt it for use with finite difference methods. We will present the methodology behind our numerical technique and some applications.
The National Research Council research associateship program supported this work.

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