The maximum entropy moment closure for the two-moment approximation of the radiative transfer equation is presented. The resulting moment equations, known as the M1 model, are solved using a finite-volume method with adaptive mesh refinement (AMR) and two Riemann-solver based flux function solvers: a Roe-type and a Harten-Lax van Leer (HLL) solver. Three different boundary schemes are also presented and discussed. When compared to the discrete ordinates method (DOM) in several representative one- and two-dimensional radiation transport problems, the results indicate that while the M1 model cannot accurately resolve multi-directional radiation transport occurring in low-absorption media, it does provide reasonably accurate solutions, both qualitatively and quantitatively, when compared to the DOM predictions in most of the test cases involving either absorbing-emitting or scattering media. The results also show that the M1 model is computationally less expensive than DOM for more realistic radiation transport problems involving scattering and complex geometries.

The maximum entropy moment closure for the two-moment approximation of the radiative transfer equation is presented. The resulting moment equations, known as the M1 model, are solved using a finite-volume method with adaptive mesh refinement (AMR) and two Riemann-solver based flux function solvers: a Roe-type and a Harten-Lax van Leer (HLL) solver. Three different boundary schemes are also presented and discussed. When compared to the discrete ordinates method (DOM) in several representative one- and two-dimensional radiation transport problems, the results indicate that while the M1 model cannot accurately resolve multi-directional radiation transport occurring in low-absorption media, it does provide reasonably accurate solutions, both qualitatively and quantitatively, when compared to the DOM predictions in most of the test cases involving either absorbing-emitting or scattering media. The results also show that the M1 model is computationally less expensive than DOM for more realistic radiation transport problems involving scattering and complex geometries.