Related papers: A Second Order Radiative Transfer Equation and Its…
The computation of the radiative transfer equation is expensive mainly due to two stiff terms: the transport term and the collision operator. The stiffness in the former comes from the fact that particles (such as photons) travels at the…
Can graded meshes yield more accurate numerical solution than uniform meshes? A time-dependent nonlocal diffusion problem with a weakly singular kernel is considered using collocation method. For its steady-state counterpart, under the…
Highly precise numerical solutions to the radiative transfer equation with polarization present a special challenge. Here, we establish a precise numerical solution to the radiative transfer equation with combined Rayleigh and isotropic…
The porous medium equation (PME) is a typical nonlinear degenerate parabolic equation. An energetic variational approach has been studied in a recent work [6], in which the trajectory equation is obtained, and a few first order accurate…
Numerical solutions of the cosmic-ray (CR) magneto-hydrodynamic equations are dogged by a powerful numerical instability, which arises from the constraint that CRs can only stream down their gradient. The standard cure is to regularize by…
Simple finite differencing of the anisotropic diffusion equation, where diffusion is only along a given direction, does not ensure that the numerically calculated heat fluxes are in the correct direction. This can lead to negative…
Heterogeneous anisotropic diffusion problems arise in the various areas of science and engineering including plasma physics, petroleum engineering, and image processing. Standard numerical methods can produce spurious oscillations when they…
The radiative transfer equation (RTE) is a cornerstone for describing the propagation of electromagnetic radiation in a medium, with applications spanning atmospheric science, astrophysics, remote sensing, and biomedical optics. Despite its…
We describe a novel Godunov-type numerical method for solving the equations of resistive relativistic magnetohydrodynamics. In the proposed approach, the spatial components of both magnetic and electric fields are located at zone interfaces…
The radiative transfer equation models the interaction of radiation with scattering and absorbing media and has important applications in various fields in science and engineering. It is an integro-differential equation involving time,…
Numerical methods for solving the ideal magnetohydrodynamic (MHD) equations in more than one space dimension must either confront the challenge of controlling errors in the discrete divergence of the magnetic field, or else be faced with…
Exact space-time propagator for the wave (second-order in time) equation in a layered system, made up of a layer sandwiched between two other different semi-infinite layers, is obtained by means of the multiple scattering theory (MST)…
This paper presents a matrix formulation of the scalar laws of radiative transfer. The method applies to coupled mixed boundary condition problems on general domains. Participating media can range from transparent to absorbing, emitting,…
This paper presents an overview of the radiative transfer problem of calculating the spectral line intensity and polarization that emerges from a (generally magnetized) astrophysical plasma composed of atoms and molecules whose excitation…
In this work, a steady discrete unified gas kinetic scheme (SDUGKS) is proposed to solve the steady radiative transfer equation (RTE), which is an improvement of the original SDUGKS [X. F. Zhou et al., J. Comput. Phys. 423, 109767 (2020)].…
The study of radiative heat transfer in particulate system is usually based on radiative transfer equation (RTE) with effective radiative properties. However, for non-random, densely and regularly packed particulate systems, the…
In this paper, we study the Helmholtz transmission eigenvalue problem for inhomogeneous anisotropic media with the index of refraction $n(x)\equiv 1$ in two and three dimension. Starting with a nonlinear fourth order formulation established…
The radiative transfer equation (RTE) for polarized light accepts a convenient exponential solution when the absorption matrix commutes with its integral. We characterize some of the matrix depth variations which are compatible with the…
Mass-conserving reaction-diffusion (MCRD) systems are widely used to model phase separation and pattern formation in cell polarity, biomolecular condensates, and ecological systems. Numerical simulations and formal asymptotic analysis…
We introduce AREPO-RT, a novel radiation hydrodynamic (RHD) solver for the unstructured moving-mesh code AREPO. Our method solves the moment-based radiative transfer equations using the M1 closure relation. We achieve second order…