A critique of the modified Levermore–Pomraning equations

The Modified Levermore–Pomraning (MLP) equations have been recently proposed by Akcasu as a treatment of transport in stochastic media with scattering. Using the bimaterial Markovian density statistics originally introduced by Pomraning, a new derivation of the MLP equations is presented for the continuous transport equation with energy dependence and ‘density’ sources. A heuristic MLP model is also introduced for calculations in finite slabs and is compared to the Levermore–Pomraning model using theoretical considerations. Numerical comparisons of the MLP and LP models are presented for a set of standard tests as well as related problems for which we give reference results.