A Two-moment Radiation Hydrodynamics Scheme Applicable to Simulations of Planet Formation in Circumstellar Disks

Abstract

We present a numerical code for radiation hydrodynamics designed as a module for the freely available PLUTO code. We adopt a gray approximation and include radiative transfer following a two-moment approach by imposing the M1 closure to the radiation fields. This closure allows for a description of radiative transport in both the diffusion and free-streaming limits, and is able to describe highly anisotropic radiation transport as can be expected in the vicinity of an accreting planet in a protoplanetary disk. To reduce the computational cost caused by the timescale disparity between radiation and matter fields, we integrate their evolution equations separately in an operator-split way, using substepping to evolve the radiation equations. We further increase the code's efficiency by adopting the reduced speed of light approximation (RSLA). Our integration scheme for the evolution equations of radiation fields relies on implicit-explicit schemes, in which radiation-matter interaction terms are integrated implicitly while fluxes are integrated via Godunov-type solvers. The module is suitable for general astrophysical computations in one, two, and three dimensions in Cartesian, spherical, and cylindrical coordinates, and can be implemented on rotating frames. We demonstrate the algorithm performance on different numerical benchmarks, paying particular attention to the applicability of the RSLA for computations of physical processes in protoplanetary disks. We show 2D simulations of vertical convection in disks and 3D simulations of gas accretion by planetary cores, which are the first of their kind to be solved with a two-moment approach.

Collapse of turbulent massive cores with ambipolar diffusion and hybrid radiative transfer

“…The FLD method is well suited for radiation transport in optically thick media, but is not adapted to strongly anisotropic radiation fields. The particular treatment of stellar radiation, also called irradiation, was later improved to track the higher-energy stellar photons and accurately compute the opacity during the first interaction of the photons with the ambient medium (Kuiper et al 2010b;Flock et al 2013;Ramsey & Dullemond 2015;Rosen et al 2017;Mignon-Risse et al 2020;Gressel et al 2020;Fuksman et al 2021).…”

VETTAM: A scheme for radiation hydrodynamics with adaptive mesh refinement using the variable Eddington tensor method

“…For instance, FLD methods cannot cast shadows (Hayes & Norman 2003;Kuiper & Klessen 2013). A more accurate closure scheme that has recently been adopted widely is the 𝑀 1 closure (e.g., González et al 2007;Aubert & Teyssier 2008;Skinner & Ostriker 2013;Rosdahl et al 2013;Rosdahl & Teyssier 2015;Kannan et al 2019;Skinner et al 2019;Bloch et al 2021;Melon Fuksman et al 2021;Chan et al 2021;Wibking & Krumholz 2021), which retains the time evolution of the radiation flux and adopts a local closure relation for the radiation pressure tensor, or equivalently the Eddington tensor, in terms of the local radiation energy density and flux; a variety of assumptions regarding the nature of the radiation field are possible, each yielding slightly different versions of the closure relation (Minerbo 1978;Levermore 1984). While the 𝑀 1 closure can handle transitions in optical depths for a single beam of radiation, it fails for other non-trivial geometrical distributions of radiation sources.…”

Neutrino flavor mixing with moments

“…quantum moments. Neutrino transport based on angular moments of the classical neutrino radiation field are already used in many state of the art supernova simulation codes due to their computational efficiency (e.g ., [60][61][62][63][64][65]). Including the quantum kinetic equations describing the evolution of the quantum moments will rely on techniques developed both in the neutrino oscillation literature and in the neutrino transport literature.…”