Numerical solution of Hyperbolic PDEs with astrophysical applications to relativistic plasmas
Dipartimento di Ingegneria Civile e Ambientale dell'Università di Trento
The numerical solution of hyperbolic partial differential equations has become a necessity in several branches of physics and applied mathematics. I will present the most modern numerical techniques that are currently adopted, based on the conservative formulation of hyperbolic equations, and with special attention to Finite Volume and to Discontinuous Galerkin Methods. As a relevant application, I will consider the equations of relativistic magnetohydrodynamics and radiation hydrodynamics, that govern both the dynamics and the emission properties in several high energy astrophysical phenomena. Some emphasis will be given to the presentation of a new high order scheme, that can equally well account for non-stiff and for stiff source-terms in the equations, as those that are encountered in the high conductivity limit of resistive relativistic magnetohydrodynamics. I will show a few specific applications, including relativistic magnetic reconnection and the accretion of radiating accretion flows around a black hole.