Second-order time evolution of PN equations for radiation transport

High-Order Entropy-Based Closures for Linear Transport in Slab Geometry II: A Computational Study of the Optimization Problem

“…The use of "numerical" scattering to regularize moment problems has been reported before in [43,50]. The regularization acts as barrier that prevents the entropyansatz from getting too close to the delta-type distributions which characterize the boundary ∂R m .…”

A new spherical harmonics scheme for multi-dimensional radiation transport I. Static matter configurations

“…These oscillations are related to the so-called Gibbs phenomenon that occurs when non-smooth functions are approximated with smooth basis functions [8]. The worst consequence of such oscillations is that they can cause the radiation intensity to become negative, which may lead to negative matter temperatures when the radiation transport is coupled to the matter energy equation [33,38]. There have been several attempts to address this problem [40,38,10,32,39,25].…”

“…The worst consequence of such oscillations is that they can cause the radiation intensity to become negative, which may lead to negative matter temperatures when the radiation transport is coupled to the matter energy equation [33,38]. There have been several attempts to address this problem [40,38,10,32,39,25]. One of the most efficient, robust, and accurate approaches is the one by McClarren & Hauck [32], in which filters are proposed to remove oscillations of the radiation intensity.…”

Robust and accurate filtered spherical harmonics expansions for radiative transfer

“…These oscillations are numerical artifacts -a by-product of approximating a non-smooth function with a smooth basis. A catastrophic consequence of these oscillations is that they can cause the radiation energy-density to become negative which, when the radiative transfer is coupled to a material equation [14,15], can cause the material temperature to become negative. Worse still, it has been shown that these negative solutions can arise in any finite-order spherical harmonics approximation [14].…”