We present a formulation and numerical algorithm to extend the scheme for gray radiation magnetohydrodynamics (MHD) developed by Jiang to include the frequency dependence via the multigroup approach. The entire frequency space can be divided into an arbitrary number of groups in the lab frame, and we follow the time-dependent evolution of frequency-integrated specific intensities along discrete rays inside each group. Spatial transport of photons is done in the lab frame while all the coupling terms are solved in the fluid rest frame. Lorentz transformation is used to connect different frames. The radiation transport equation is solved fully implicitly in time while the MHD equations are evolved explicitly so that time step is not limited by the speed of light. A finite volume approach is used for transport in both spatial and frequency spaces to conserve the radiation energy density and momentum. The algorithm includes photon absorption, electron scattering, as well as Compton scattering, which is calculated by solving the Kompaneets equation. The algorithm is accurate for a wide range of optical depth conditions and can handle both radiation-pressure- and gas-pressure-dominated flows. It works for both Cartesian and curvilinear coordinate systems with adaptive mesh refinement. We provide a variety of test problems including a radiating sphere, shadow test, absorption of a moving gas, Bondi-type flows, as well as a collection of test problems for thermal and bulk Compton scattering. We also discuss examples where frequency dependence can make a big difference compared with the gray approach.
A reduced speed-of-light (RSOL) approximation is a useful technique for magnetohydrodynamic (MHD)-particle-in-cell (PIC) simulations. With an RSOL, some ‘in-code’ speed-of-light $\tilde{c}$ is set to much lower values than the true c, allowing simulations to take larger time-steps (which are restricted by the Courant condition given the large CR speeds). However, due to the absence of a well-formulated RSOL implementation from the literature, with naive substitution of the true c with a RSOL, the CR properties in MHD-PIC simulations (e.g. CR energy or momentum density, gyro radius) vary artificially with respect to each other and with respect to the converged ($\tilde{c} \rightarrow c$) solutions, with different choices of a RSOL. Here, we derive a new formulation of the MHD-PIC equations with an RSOL and show that (1) it guarantees all steady-state properties of the CR distribution function, and background plasma/MHD quantities are independent of the RSOL $\tilde{c}$ even for $\tilde{c} \ll c$; (2) it ensures that the simulation can simultaneously represent the real physical values of CR number, mass, momentum, and energy density; (3) it retains the correct physical meaning of various terms like the electric field; and (4) it ensures the numerical time-step for CRs can always be safely increased by a factor $\sim c/\tilde{c}$. This new RSOL formulation should enable greater self-consistency and reduced CPU cost in simulations of CR–MHD interactions.
more » « less- NSF-PAR ID:
- 10372446
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Monthly Notices of the Royal Astronomical Society
- Volume:
- 516
- Issue:
- 4
- ISSN:
- 0035-8711
- Page Range / eLocation ID:
- p. 5143-5147
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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