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Simulation of magnetohydrodynamic flows - A constrained transport method
Evans, Charles R.; Hawley, John F.
AA(California Institute of Technology, Pasadena), AB(California Institute of Technology, Pasadena; Virginia, University, Charlottesville)
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 332, Sept. 15, 1988, p. 659-677. (ApJ Homepage)
Publication Date:
NASA/STI Keywords:
Computational Astrophysics, Computerized Simulation, Magnetohydrodynamic Flow, Transport Theory, Active Galactic Nuclei, Adaptive Filters, Finite Difference Theory, Grid Generation (Mathematics)
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The authors discuss an optimal strategy for treating the magnetohydrodynamic (MHD) field transport (induction) equation. The induction equation is shown to assume its simplest form when written in terms of the contra-variant forms of velocity and magnetic vector density. The authors describe a new numerical technique, called constrained transport (CT), for evolving the induction equation in a way that maintains vanishing divergence of the poloidal (constrained) field components to within machine round-off error. It is also shown how the 3+1 formalism of numerical relativity can be used to express the general relativistic MHD equations in a form suitable for numerical evolution. The relativistic form of the magnetic induction equation is then shown to fit naturally within the CT scheme. Several models involving magnetized flow near a black hole are used as calibration of the CT scheme.

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