A New Monte Carlo Method for Time-Dependent Neutrino Radiation Transport

Abstract

Monte Carlo approaches to radiation transport have several attractive properties such as 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 potentially 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 a robust approach for use in neutrino transport calculations in core-collapse supernovae. Our velocity-dependent scheme can easily be adapted to photon transport.

Light Curves and Spectra from a Unimodal Core-collapse Supernova

“…The SuperNu code has an implementation of Implicit Monte Carlo (IMC) (Fleck & Cummings 1971;Wollaber 2016) for thermal radiative transfer, and Discrete Diffusion Monte Carlo (DDMC) (Densmore et al 2007(Densmore et al , 2012Abdikamalov et al 2012) to accelerate IMC in optically thick regions of phase space. SuperNu has features specialized for homologous outflows and structured opacity (Wollaeger et al 2013;Wollaeger & Van Rossum 2014).…”

“…Considerable effort has been invested in developing software that is capable of accurately simulating multidimensional neutrino radiation-hydrodynamics in the presence of gravity (see, for instance, Livne (1993) ;Fryxell et al (2000); Fryer et al (2006); Burrows et al (2006); Ott et al (2008); Almgren et al (2010); Zhang et al (2011);Abdikamalov et al (2012); Zhang et al (2013); Dolence et al (2015)) and performing computationally intensive studies with this software (Fryer & Warren 2002;Fryer & Young 2007;Burrows et al 2012;Bruenn et al 2013;Couch 2013;Couch & Ott 2013;Dolence et al 2015;Couch et al 2015). For recent reviews of the CCSN field, see Janka (2012); Burrows (2013); Janka et al (2016); Müller (2017).…”

A new spherical harmonics scheme for multi-dimensional radiation transport I. Static matter configurations

“…Finally, we consider the 3D homogeneous sphere problem, which is frequently employed to test radiation transport codes [46,44,3]. This problem consists of a static homogeneous and isothermal sphere of radius R that radiates in vacuum.…”

“…Monte-Carlo methods (e.g., [20,21,3]) are often regarded as the most accurate method for radiation transport, but they are also not without drawbacks: Monte-Carlo solutions exhibit statistical noise due to the finite sampling of the phase space. Since this noise decreases only as N −1/2 , where N is the number of Monte Carlo particles, it can take many particles to produce a sufficiently smooth solution, making large simulations computationally very expensive.…”

MODA: a new algorithm to compute optical depths in multidimensional hydrodynamic simulations

“…Codes that solve the Boltzmann equations, through either finite difference (e.g., the discrete ordinate method, see Liebendörfer et al 2004 in 1D;Ott et al 2008 in 2D;Sumiyoshi & Yamada 2012 in 3D) or spectral methods (e.g., the spherical harmonic method, see Peres et al 2014), Monte-Carlo codes (e.g., Abdikamalov et al 2012), and most approximative schemes, such as flux-limited diffusion (e.g., Whitehouse et al 2005;Swesty & Myra 2009) or M1 schemes (e.g., Shibata & Taniguchi 2011;O'Connor & Ott 2013), do not need to compute τ separately, since it is a physical quantity that results from the algorithm itself. Other codes, such as that of Kuroda et al (2012), which also employs the M1 closure of the transport equations using a variable Eddington factor, calculate τ assuming that radiation moves along radial paths.…”