Multilevel discontinuous Galerkin methods for LTE radiative transfer in heterogeneous media

Radiative transfer problems in astrophysical applications, for instance in circumstellar clouds, are characterized by extreme parameter changes over highly varying scales. Adding to this the 6-dimensional phase space and bad conditioning of the problems, accurate simulation of such problems is highly challenging even on high performance computers. In this project, we focus on radiation fields coupled in a nonlinear way (local thermodynamic equilibrium) to a temperature field. The discretization and solution algorithms are based on recent developments of multilevel discontinuous Galerkin methods for the grey approximation. Since the problem at hand involves serveral hundred coupled unknowns in every point in space, a major aspect of this project is the efficient, matrix-free implementation on high performance computers. Data for circumstellar clouds is used for benchmarking our developments, but the methods have much wider applicatbility.

Name and contact of project responsible(s):

Prof. Dr. Guido Kanschat (Interdisciplinary Center for Scientific Computing, Heidelberg University)
Prof. Dr. Cornelis P. Dullemond (Institute for Theoretical Astrophysics (ITA), Heidelberg University)
Pablo Lucero Lorca (Interdisciplinary Center for Scientific Computing, Heidelberg University)

Involved scientists and partners

Prof. Jean C. Ragusa (Nuclear Engineering, Texas A&M University)
Prof. Blanca Ayuso de Dios (Mathematics Department, Bologna University)

Publications:

W. Bangerth, T. Heister, L. Heltai, G. Kanschat, M. Kronbichler, M.
Maier, B. Turcksin & T. D. Young
The deal.II Library, Version 8.1
arXiv preprint. 2013

Kanschat, G. & Ragusa, J. C.
A Robust Multigrid Preconditioner for SNDG Approximation of
Monochromatic, Isotropic Radiation Transport Problems
SIAM J. Sci. Comput. 36(5) , pp.2326-2345. 2014

Morel, J. E., Ragusa, J. C., Adams, M. L. & Kanschat, G.
Asymptotic PN-equivalent SN+1equations
Transport Theory Stat. Phys. 42(1) , pp.3-20. 2013

Ragusa, J., Guermond, J.-L. & Kanschat, G.
A robust Sn-DG-approximation for radiation transport in optically
thick and diffusive regimes
J. Comput. Phys. 231(4) , pp.1947–1962. 2012

Guermond, J.-L. & Kanschat, G.
Asymptotic analysis of upwind DG approximation of the radiative
transport equation in the diffusive limit
SIAM J. Numer. Anal. 48(1) , pp.53-78. 2010