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Published March 13, 2012 | Submitted
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A New Monte Carlo Method for Time-Dependent Neutrino Radiation Transport


Monte Carlo approaches to radiation transport have several attractive properties compared to deterministic methods. These include simplicity of implementation, high accuracy, and good parallel scaling. Moreover, Monte Carlo methods can handle complicated geometries and are relatively easy to extend to multiple spatial dimensions, which makes them particularly interesting in modeling complex multi-dimensional astrophysical phenomena such as core-collapse supernovae. The aim of this paper is to explore Monte Carlo methods for modeling neutrino transport in core-collapse supernovae. We generalize the implicit Monte Carlo photon transport scheme of Fleck & Cummings and gray discrete-diffusion scheme of Densmore et al. to energy-, time-, and velocity-dependent neutrino transport. Using our 1D spherically-symmetric implementation, we show that, similar to the photon transport case, the implicit scheme enables significantly larger timesteps compared with explicit time discretization, without sacrificing accuracy, while the discrete-diffusion method leads to significant speed-ups at high optical depth. Our results suggest that a combination of spectral, velocity-dependent, implicit Monte Carlo and discrete-diffusion Monte Carlo methods represents an attractive approach for use in neutrino radiation-hydrodynamics simulations of core-collapse supernovae. Our velocity-dependent scheme can easily be adapted to photon transport.

Additional Information

We are happy to acknowledge helpful exchanges with Timothy Brandt, Jeffery Densmore, Peter Diener, Roland Haas, Daniel Kasen, Oleg Korobkin, and Christian Reisswig. This work was supported in part by NSF under grant nos. AST-0855535, OCI-0905046, OCI 0721915, OCI 0725070, OCI 0905046, OCI 0941653, PIF-0904015, PHY-0960291, and TG-PHY100033, by the DOE under grant DE-FG02- 08ER41544, and by the Sherman Fairchild Foundation. Results presented in this article were obtained through computations on machines of the Louisiana Optical Network Initiative under grant loni_numrel07, on the Caltech compute cluster "Zwicky" (NSF MRI award No. PHY-0960291), on the NSF Teragrid under grant TG-PHY100033, and at the National Energy Research Scientific Computing Center (NERSC), which is supported by the Office of Science of the US Department of Energy under contract DE-AC03-76SF00098.

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