Transport equations in moving material Part I: Neutrons and photons

Spectral convergence of the generalized Polynomial Chaos reduced model obtained from the uncertain linear Boltzmann equation

“…They express the probability for a particle to interact with the medium (to be absorbed, scattered, to encounter a particular reaction etc.). The cross-sections, in a sense, contain all the physics (which is kind of hidden in this paper): they can be related to other coupled physics such as reactive flows, isotopic depletion [17] in neutronics, temperature dependence for photonics [51] or media subject to material motion [64] (neutronics, photonics, plasma physics). Those physics may communicate uncertainties to the particle transport via the cross-sections.…”

Neutron transport in Eulerian coordinates with bulk material motion

“…For non-relativistic neutrons, where Galilean invariance is valid, there have been two historical approaches to dealing with the corrections necessary for transport against a moving material background. In the first approach, recognizing that neutron interaction rates are frame invariant, "effective" cross sections (and "effective" sources, if necessary) are formed using stationary cross section data scaled by the relative to lab frame velocities and a velocity Jacobian (Wienke et al, 1987a;Wienke and Hill, 1990;Wienke, 2005 ). While this approach allows the neutron transport solution to be performed within the lab frame, the resulting "effective" cross sections in this frame are now anisotropic for all reactions, including total removal and fission, with associated complications and potential instabilities in the transport solution.…”

“…The second approach transforms the solution of the transport equation to the co-moving frame, i.e., the reference frame where neutrons interact with the bulk material as if it were stationary (Wienke, 1974(Wienke, , 2005Wienke et al, 1987b). This transformation results in a transport equation with a pseudo-acceleration term generated by material acceleration (spatial or temporal) and a material velocity effect term.…”