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A mathematical description of the IDSA for supernova neutrino transport, its discretization and a comparison with a finite volume scheme for Boltzmann’s equation
Heiko Berninger1 ; Emmanuel Frénod2 ; Martin J. Gander1 ; Matthias Liebendörfer3 ; Jérôme Michaud1 ; Nicolas Vasset3
1Université de Genève, Section de Mathématiques, 2-4, rue du Lièvre, CP 64, CH-1211, Genève
2Université de Bretagne-Sud, Laboratoire de Mathématiques, Centre Yves Coppens, Bat. B, BP 573, F-56017 Vannes
3Universität Basel, Departement Physik, Klingelbergstrasse 82, CH-4056 Basel
ESAIM. Proceedings, Tome 38 (2012), pp. 163-182
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In this paper we give an introduction to the Boltzmann equation for neutrino transport used in core collapse supernova models as well as a detailed mathematical description of the Isotropic Diffusion Source Approximation (IDSA) established in [6]. Furthermore, we present a numerical treatment of a reduced Boltzmann model problem based on time splitting and finite volumes and revise the discretization of the IDSA in [6] for this problem. Discretization error studies carried out on the reduced Boltzmann model problem and on the IDSA show that the errors are of order one in both cases. By a numerical example, a detailed comparison of the reduced model and the IDSA is carried out and interpreted. For this example the IDSA modeling error with respect to the reduced Boltzmann model is numerically determined and localized.
DOI : 10.1051/proc/201238009

Heiko Berninger  1   ; Emmanuel Frénod  2   ; Martin J. Gander  1   ; Matthias Liebendörfer  3   ; Jérôme Michaud  1   ; Nicolas Vasset  3

1 Université de Genève, Section de Mathématiques, 2-4, rue du Lièvre, CP 64, CH-1211, Genève 
2 Université de Bretagne-Sud, Laboratoire de Mathématiques, Centre Yves Coppens, Bat. B, BP 573, F-56017 Vannes 
3 Universität Basel, Departement Physik, Klingelbergstrasse 82, CH-4056 Basel  
@article{EP_2012_38_a8,
     author = {Heiko Berninger and Emmanuel Fr\'enod and Martin J. Gander and Matthias Liebend\"orfer and J\'er\^ome Michaud and Nicolas Vasset},
     title = {A mathematical description of the {IDSA} for supernova neutrino transport, its discretization and a comparison with a finite volume scheme for {Boltzmann{\textquoteright}s} equation},
     journal = {ESAIM. Proceedings},
     pages = {163--182},
     year = {2012},
     volume = {38},
     doi = {10.1051/proc/201238009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201238009/}
}
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Heiko Berninger; Emmanuel Frénod; Martin J. Gander; Matthias Liebendörfer; Jérôme Michaud; Nicolas 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. Proceedings, Tome 38 (2012), pp. 163-182. doi: 10.1051/proc/201238009

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