MOCMC: Method of Characteristics Moment Closure, a Numerical Method for Covariant Radiation Magnetohydrodynamics

Abstract

We present a conservative numerical method for radiation magnetohydrodynamics with frequencydependent full transport in stationary spacetimes. This method is stable and accurate for both large and small optical depths and radiation pressures. The radiation stress-energy tensor is evolved in fluxconservative form, and closed with a swarm of samples that each transport a multigroup representation of the invariant specific intensity along a null geodesic. In each zone, the enclosed samples are used to efficiently construct a Delaunay triangulation of the unit sphere in the comoving frame, which in turn is used to calculate the Eddington tensor, average source terms, and adaptively refine the sample swarm. Radiation four-fources are evaluated in the moment sector in a semi-implicit fashion. The radiative transfer equation is solved in invariant form deterministically for each sample. Since each sample carries a discrete representation of the full spectrum, the cost of evaluating the transport operator is independent of the number of frequency groups, representing a significant reduction of algorithmic complexity for transport in frequency dependent problems. The major approximation we make in this work is performing scattering in an angle-averaged way, with Compton scattering further approximated by the Kompaneets equation. Despite relying on particles to solve the radiative transfer equation, the scheme is efficient and stable for both large optical depths and small ratios of gas to radiation pressure. Local adaptivity in samples also makes this scheme more amenable to nonuniform meshes than a traditional Monte Carlo method. We describe the method and present results on a suite of test problems. We find that MOCMC converges at least as ∼ N −1 , rather than the canonical Monte Carlo N −1/2 , where N is the number of samples per zone. Isotropic one-zone problems have no shot noise at all. On several problems we demonstrate substantial improvement over Eddington and M1 closures and gray opacities. arXiv:1907.09625v1 [astro-ph.HE]

A New Moment-Based General-Relativistic Neutrino-Radiation Transport Code: Methods and First Applications to Neutron Star Mergers

“…Other methods solving the full-Boltzmann equation of radiation transport equations in seven dimensions include the short characteristic method (Davis et al 2012), the 𝑆 𝑁 schemes of Nagakura et al (2014) and Chan & Müller (2020), the 𝐹𝑃 𝑁 approach (McClarren & Hauck 2010;Radice et al 2013), the lattice Boltzmann method (Weih et al 2020b), and the recently proposed method of characteristics moment closure (MOCMC) method (Ryan & Dolence 2019). All of these approaches can, in principle, model the full range of conditions and effects encountered in NS mergers.…”

General Relativistic Implicit Monte Carlo Radiation-hydrodynamics

“…Decades of progress have seen the field of computational physics advance from relatively simple N-body and hydrodynamics simulations to the point where relativistic magnetohydrodynamics (MHD) together with radiation treatments beyond the diffusion approximation have become commonplace (a far from complete list includes such works as Farris et al 2008;Müller et al 2010;Shibata et al 2011;Zanotti et al 2011;Saḑowski et al 2013;McKinney et al 2014;Tominaga et al 2015;Kuroda et al 2016;Ryan & Dolence 2020). A historical perspective of this progress is exemplified by our own contributions with the Cosmos ++ code, which grew in sophistication from a modest start in Newtonian hydrodynamics and flux-limited (gray) diffusion (Anninos et al 2003) to eventually incorporate general relativistic magneto-hydrodynamics on unstructured, adaptively refined grids (Anninos et al 2005).…”

General Relativistic Implicit Monte Carlo Radiation-Hydrodynamics

“…Decades of progress has seen the field of computational physics advance from relatively simple N-body and hydrodynamics simulations to the point where relativistic magneto-hydrodynamics (MHD) together with radiation treatments beyond the diffusion approximation have become common place (a far from incomplete list includes Farris et al 2008;Müller et al 2010;Shibata et al 2011;Zanotti et al 2011;Sadowski et al 2013;McKinney et al 2014;Tominaga et al 2015;Kuroda et al 2016;Ryan & Dolence 2020). A historical perspective of this progress is exemplified by our own contributions with the Cosmos++ code, which grew in sophistication from a modest start in Newtonian hydrodynamics and flux-limited (grey) diffusion (Anninos et al 2003), to eventually incorporate general relativistic magneto-hydrodynamics on unstructured, adaptively refined grids (Anninos et al 2005).…”