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Finite Element Method for Capturing Ultra-relativistic ShocksWhile finite element methods are used extensively by researchers solving computational fluid dynamics in fields other than astrophysics, their use in astrophysical fluid simulations has been predominantly overlooked. Current simulations using other methods such as finite difference and finite volume (based on finite difference) have shown remarkable results, but these methods are limited by their fundamental properties in aspects that are important for simulations with complex geometries and widely varying spatial and temporal scale differences. We have explored the use of finite element methods for astrophysical fluids in order to establish the validity of using such methods in astrophysical environments. We present our numerical technique applied to solving ultra-relativistic (Lorentz Factor Gamma >> 1) shocks which are prevalent in astrophysical studies including relativistic jets and gamma-ray burst studies. We show our finite element formulation applied to simulations where the Lorentz factor ranges up to 2236 and demonstrate its stability in solving ultra-relativistic flows. Our numerical method is based on the Flowfield Dependent Variation (FDV) Method, unique in that numerical diffusion is derived from physical parameters rather than traditional artificial viscosity methods. Numerical instabilities account for most of the difficulties when capturing shocks in this regime. Our method results in stable solutions and accurate results as compared with other methods.
Document ID
20030062240
Acquisition Source
Marshall Space Flight Center
Document Type
Preprint (Draft being sent to journal)
Authors
Richardson, G. A.
(National Space Science and Technology Center Huntsville, AL, United States)
Chung, T. J.
(Alabama Univ. Huntsville, AL, United States)
Date Acquired
August 21, 2013
Publication Date
January 1, 2003
Subject Category
Astrophysics
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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