Related papers: A two-streams discrete ordinates solution of radia…
A new set of discrete ordinates is proposed for one-dimensional radiative transfer in spheres with central symmetry. The set is structured with un-normalized circular functions. This resulted in a conservative and closed set of discrete…
A nonsingular analytical solution for the transfer equation in a pure absorber is obtained in central symmetry and in a monochromatic radiation field. The native regular singularity of the equation is removed by applying a linear…
The transfer equation in spherical geometry with central symmetry, which is a partial differential equation in two variables r and m, is reduced to a one-dimensional transfer equation in r parametric in m. This is done by dropping the…
The discrete ordinates method (DOM) of solution to the 1D radiative transfer equation has been an effective method of solution for nearly 70 years. During that time, the method has experienced numerous improvements as numerical and…
A fourth-order dispersive flow equation for closed curves on the canonical two-dimensional unit sphere arises in some contexts in physics and fluid mechanics. In this paper, a geometric generalization of the sphere-valued model is…
We present a comprehensive analytical study of radiative transfer using the method of moments and include the effects of non-isotropic scattering in the coherent limit. Within this unified formalism, we derive the governing equations and…
Space fractional convection diffusion equation describes physical phenomena where particles or energy (or other physical quantities) are transferred inside a physical system due to two processes: convection and superdiffusion. In this…
The discrete ordinates method with angular parameters is discussed in light of the recent extension of its underlying hypothesis. The analysis shows that the method, although it compares very well with the trajectory of photons model, it…
The radiative transfer equation (RTE) arises in many different areas of science and engineering. In this paper, we propose and investigate a discrete-ordinate discontinuous-streamline diffusion (DODSD) method for solving the RTE, which is a…
Observations and magnetohydrodynamic simulations of solar and stellar atmospheres reveal an intermittent behavior or steep gradients in physical parameters, such as magnetic field, temperature, and bulk velocities. The numerical solution of…
We present a novel generalization of the two-stream method of radiative transfer, which allows for the accurate treatment of radiative transfer in the presence of strong infrared scattering by aerosols. We prove that this generalization…
This paper presents a new resolution strategy for multi-scale streamer discharge simulations based on a second order time adaptive integration and space adaptive multiresolution. A classical fluid model is used to describe plasma…
The problem of two stiff fluids (energy density = pressure) moving radially in spherical symmetry is treated. The metric ansatz is chosen spherically symmetric, conformally static with a multiplicative separation of variables. The first…
Two-stream radiative transfer is a workhorse in the Earth, planetary and exoplanetary sciences due to its simplicity and ease of implementation. However, a longstanding limitation of the two-stream approximation is its inaccuracy in 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…
This work presents efficient solution techniques for radiative transfer in the smoothed particle hydrodynamics discretization. Two choices that impact efficiency are how the material and radiation energy are coupled, which determines the…
We study the direct and an inverse source problem for the radiative transfer equation arising in optical molecular imaging. We show that for generic absorption and scattering coefficients, the direct problem is well-posed and the inverse…
We present a fast, high-order accurate and adaptive boundary integral scheme for solving the Stokes equations in complex---possibly nonsmooth---geometries in two dimensions. The key ingredient is a set of panel quadrature rules capable of…
A new numerical method to solve an inverse source problem for the radiative transfer equation involving the absorption and scattering terms, with incomplete data, is proposed. No restrictive assumption on those absorption and scattering…
We develop a new numerical scheme for solving the radiative transfer equation in a spherically symmetric system. This scheme does not rely on any kind of diffusion approximation and it is accurate for optically thin, thick, and intermediate…