Kinetic Scheme for Solving M1 Model of Radiative Transfer

Abstract

We show a numerical scheme to solve the moment equations of the radiative transfer, i.e., M1 model which follows the evolution of the energy density, $E$, and the energy flux, $ \mbox{\boldmath$F$} $. In our scheme we reconstruct the intensity from $E$ and $ \mbox{\boldmath$F$} $ so that it is consistent with the closure relation, relation, $\chi =(3+4f^2)/(5+2\sqrt{4-3f^2})$. Here the symbols, $\chi$, $ f = |\mbox{\boldmath$F$}|/(cE) $, and $c$, denote the Eddington factor, the reduced flux, and the speed of light, respectively. We evaluate the numerical flux across the cell surface from the kinetically reconstructed intensity. It is an explicit function of $E$ and $ \mbox{\boldmath$F$} $ in the neighboring cells across the surface considered. We include absorption and reemission within a numerical cell in the evaluation of the numerical flux. The numerical flux approaches to the diffusion approximation when the numerical cell itself is optically thick. Our numerical flux gives a stable solution even when some regions computed are very optically thick. We show the advantages of the numerical flux with examples. They include flash of beamed photons and irradiated protoplanetary disks.

32 pages, 14 figures to appear in PASJ

References in corpus (4)

• Direct Imaging of Fine Structures in Giant Planet Forming Regions of the Protoplanetary Disk around AB Aurigae
• Mid-IR imaging of the transitional disk of HD169142: Measuring the size of the gap
• Numerical Calculation of Convection with Reduced Speed of Sound Technique
• ARGOT: Accelerated radiative transfer on grids using oct-tree

Cited by in corpus (8)

• Three-Dimensional General Relativistic Radiation Magnetohydrodynamical Simulation of Super-Eddington Accretion, using a new code HARMRAD with M1 Closure
• A New Multi-Energy Neutrino Radiation-Hydrodynamics Code in Full General Relativity and Its Application to Gravitational Collapse of Massive Stars
• Formation of Overheated Regions and Truncated Disks around Black Holes; Three-dimensional General Relativistic Radiation-magnetohydrodynamics Simulations
• Supercritical Accretion onto a Non-Magnetized Neutron Star: Why is it Feasible?
• Component of energy flow from supercritical accretion disks around rotating stellar mass black holes
• Detailed modeling of dust distribution in the disk of HD 142527
• Modeling of Thermal Emission from ULX Pulsar Swift J0243.6+6124 with General Relativistic Radiation MHD simulations
• GR-RMHD Simulations of Super-Eddington Accretion Flows onto a Neutron Star with Dipole and Quadrupole Magnetic Fields