The General Relativistic Astophysical Flow Calculation Using the Flowfield-Dependent Variation Method
Dr. T.J. Chung
Department of Mechanical and Aerospace Engineering
University of Alabama in Huntsville
September 21, 2001
The general theory of relativity advanced by Einstein in 1916 remains today as the primary guiding principle for studying the gravitational radiation, neutron stars, black holes, and cosmology. Only in recent years have the partial differential equations of general relativity been met with a challenge for developing efficient numerical solution schemes. Difficulties arise from the fact that numerical schemes are controlled by four dimensional space-time metric in addition to physical complications such as shock waves, magnetohydrodynamic turbulent fluctuations, and radiative energy.
Reviews of basic underlying principles for the general relativity will be followed by the recently developed computational approach, called "The Flowfield-Dependent Variation (FDV) Method". It is shown that FDV can be implemented using the standard methods of computational fluid dynamics such as finite difference methods, finite element methods, or finite volume methods. Some computational results on relativistic shock tubes and black hole accretion problems are demonstrated.
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