We derived analytical solutions of the simplified spherical harmonics equations, an approximation of the radiative transfer equation, for infinitely extended scattering media. The derived equations are simple (sum of exponential functions) and quickly evaluated. We compared the solutions with Monte Carlo simulations in the steady-state and time domains and found much better agreement compared t...

Turbulent radiation interaction (TRI) effects are associated with the differences in the time scales of the fluid dynamic equations and the radiative transfer equations. Solving on the fluid dynamic time step size produces large changes in the radiation field over the time step. We have modified the statistically homogeneous, non-premixed flame problem of Deshmukh et al. [1] to include coal-typ...

We present an algorithm that provides a frequency-domain solution of the equation of radiative transfer (ERT) for heterogeneous media of arbitrary shape. Although an ERT is more accurate than a diffusion equation, no ERT code for the widely employed frequency-domain case has been developed to date. In this work the ERT is discretized by a combination of discrete-ordinate and finite-volume metho...

In 2009 a major next step was made in our effort to develop a two-dimensional (2D) radiation-hydrodynamics code for laser plasma simulations, namely, a new scheme for solving the radiation transport equation has been constructed and tested. The new code has been named RALEF-2D (Radiative Arbitrary LagrangianEulerian Fluid dynamics). The RALEF-2D code is based on the CAVEAT hydrodynamics package...

Using the principle of energy conservation and laws of geometrical optics, we derive the photon transport equation for turbid biological media with spatially varying isotropic refractive index. We show that when the refractive index is constant, our result reduces to the standard radiative transfer equation and when the medium is lossless and free of scattering to the well known geometrical opt...

An ADO (analytical discrete ordinates) solution is used to establish a concise and accurate result for a basic radiative transfer problem in a finite layer described by the grey equation of transfer with general anisotropic scattering. As a specific application, the solution is evaluated for the case of Fresnel boundary conditions to yield numerical results (of a high standard) for several spec...

The discrete-ordinates method is formulated to solve transient radiative transfer with the incorporation of a transient term in the transfer equation in two-dimensional rectangular enclosures containing absorbing, emitting, and anisotropically scattering media subject to diffuse and/or collimated laser irradiation. The governing equations resulting from the discrete-ordinates discretization of ...

We propose in this work a fast numerical algorithm for solving the equation of radiative transfer (ERT) in isotropic media. The algorithm has two steps. In the first step, we derive an integral equation for the angularly averaged ERT solution by taking advantage of the isotropy of the scattering kernel, and solve the integral equation with a fast multipole method (FMM). In the second step, we s...

In this paper we present a characteristic method for solving the transfer equation in differentially moving media in a curved spacetime. The method is completely general, but its capabilities are exploited at best in presence of symmetries, when the existence of conserved quantities allows to derive analytical expressions for the photon trajectories in phase space. In spherically–symmetric, sta...

Two-frequency Wigner distribution is introduced to capture the asymptotic behaviour of the space–frequency correlation of paraxial waves in the radiative transfer limits. The scaling limits give rises to deterministic transport-like equations. Depending on the ratio of the wavelength to the correlation length the limiting equation is either a Boltzmann-like integral equation or a Fokker–Planck-...