Graduate Seminar "Aktuelle Themen der Numerik"

Thursday, Jun 20, 2013 02:00 pm

Asymptotic Expansions of Boltzmann's Equation for Neutrino Transport in Core Collapse Supernovae

Dr. Heiko Berninger (Université de Genève)
Joint work with:
Emmanuel Frénod (Université de Bretagne-Sud)
Matthias Liebendörfer and Nicolas Vasset (Universität Basel)
Martin J. Gander and Jérôme Michaud (Université de Genève)

Abstract:
Simulations of core collapse supernovae require to model the radiative transfer of neutrinos. If the full Boltzmann equation is chosen as the model, computation times increase dramatically in regimes in which high density of neutrinos, i.e., small mean free paths prevail. In core collapse supernovae, neutrinos are trapped by the matter in high density regimes, where they are in diffusion, whereas they are practically freely streaming in low density regimes further away from the core. In both cases, the Boltzmann equation can be reduced considerably. This leads to the idea of a decomposition of the neutrino distribution function into trapped and streaming particle components used in the Isotropic Dffusion Source Approximation (IDSA) of Boltzmann’s equation [1].

In this talk, we will give an introduction into the IDSA in spherical symmetry, both from a physical and a mathematical point of view.  The mainpurpose of the talk will be to present a derivation of the IDSA by asymptotic analysis applying Chapman–Enskog and Hilbert expansions [2]. Finally, computational aspects and numerical solution techniques for the IDSA and the Boltzmann equation will be mentioned and numerical results for some test cases will be shown [3].

[1] M. Liebendörfer, S.C. Whitehouse, and T. Fischer. The Isotropic Diffusion Source Approximation for Supernova neutrino Transport. Astrophysical Journal, 698:1174–1190, 2009.
[2] H. Berninger, E. Frénod, M.J. Gander, M. Liebend¨orfer, J. Michaud. Derivation of the Isotropic Dffusion Source Approximation (IDSA) for Supernova Neutrino Transport by Asymptotic Expansions. To appear in SIAM Journal on Mathematical Analysis (SIMA).
[3] H. Berninger, E. Frénod, M.J. Gander, M. Liebendörfer, J. Michaud, N. Vasset.  A Mathematical Description of the IDSA for Supernova Neutrino transport, its discretization and a comparison with a finite volume scheme for Boltzmann’s Equation.  ESAIM: Proc., Vol.  38, 2012, CEMRACS ’11:  Multiscale Coupling of Complex Models in Scientific Computing, pp. 163–182.

Time: 02:00 pm

Location: Room 149, Hauptgebäude, RWTH Aachen, Templergraben 55, 52056 Aachen