Initial and boundary conditions for diffusive linear transport problems

Abstract

The initial and boundary layer analyses of an asymptotic expansion that yields a diffusive description of linear particle transport are carried out in some generality. This yields initial and boundary conditions that apply to the diffusion equation previously reported in the literature. Effects treated include boundary curvature, the variation of the transport boundary condition along the bounding surface, and spatial and temporal variations of the interaction coefficients (cross sections) in the initial and boundary layers.

A hybrid transport-diffusion Monte Carlo method for frequency-dependent radiative-transfer simulations

“…(17), (25), (27), and (28) and again neglect the spatial dependence of the normalized Planck function through the material temperature as discussed previously, we obtain…”

A Spatial Discretization Scheme for Solving the Transport Equation on Unstructured Grids of Polyhedra

“…Comparing the pez and fpz terms against equation (18) we see that our pez and fpz closures will need to have the following property. …”

“…Note that equation (18) can be rewritten in the simpler form shown in equation (14) that is used for this analysis. …”

“…The remaining three closures are designed to meet our requirement to limit to Palmer's expression for the net current across the fez face from equation (18 …”

“…We use equation (18) to express the fez current in terms of the leading-order scalar flux. Note that equation (18) can be rewritten in the simpler form shown in equation (14) that is used for this analysis.…”