This is the one of oldest fields where the scaling heterogeneous methods are approximate and the "customized modeling" flourishing.
At the same time it is obvious that this field requires the simultaneous unified methodology to treat the traditional thermal physics homogeneous models along with the electrodynamics governing equations, statements etc. This is actually well developed for the homogeneous physics. Not to say something close enough about the Heterogeneous Electrodynamics Radiative transport.
The only professor at MAE department of UCLA - G.Pomraning, had started in the 90s to footstep in the science of Nuclear Physics (Neutron Transport Theory (NTT), etc.) following the HSP-VAT developments in what was known as a linear processes averaging. Pomraning with co-authors commenced to recognize that the particle (neutron included) transport equations are actually allegedly accepted as averaged and in a few papers in the middle of the 90s they timidly gave another kind of radiative (neutron meant first of all) transport equation for a two-phase (biphasic, binary) medium.
He never consulted or talked to me regarding this area of physics, and as a result his equations were developed incorrectly. I told to I.Catton on the issue, but he did not want to be a middle man, still probably he was because they were in a friendly relations. That was all before prof. G.Pomraning passed away.
Unless the theory advanced toward inclusion of heterogeneous electrodynamics into a treatable area, the models and governing equations for radiative transport in heterogeneous media would be incomplete.
In the late 90s the HSP-VAT has been advanced by me and for Heterogeneous Electrodynamics that opened the window to work, study some aspects of radiative transport in Heterogenous media as the two (at least) scale phenomena along and using the needed formulations from Heterogeneous Electrodynamics.
As I put forward through the years, the idea that the HSP-VAT is the foundation, which is so far
the only hierarchical theoretical approach for any heterogeneous physics field,
in the following study few major steps advancing radiative transport description
via the VAT were published in
RADIATION HEAT TRANSPORT IN POROUS MEDIA (240K),
Travkin, V.S., and I. Catton, "Radiation Heat Transport in Porous Media,"
in Proc. ASME, HTD 364 3, Vol. 3, pp. 31 40, (1999).
In this the first of the kind of non-local, averaged particle transport governing equation I tried to depict the one possible scaled VAT method, one theoretical (well, the only correct for heterogeneous media) approach to describe the Upper scale radiative transport in heterogeneous media through the VAT techniques.
It should be mentioned that in that work were still accepted the initial conceptual solution of particle transport governing equation through the Boltzmann equation. This transport equation later on was proven to be incorrect - yes, the Boltzmann's particle transport equation is incorrect, see on this in - "Boltzmann Equation is Invalid in the Derivation. More than 100 Years of Misled Research? "
We will open some advancements and discussion on the issues of Heterogeneous nuclear physics
and neutron ( other particles) transport in Heterogeneous media in the section -
"Nuclear Energy,
Polyscale Polyphase
Structure of Heat Generation and HEx in LWR and HGCR. HtHr Modeling."
Comparative to the some other physical disciplines and fields this one is greatly underdeveloped.