Positivity-Preserving Linear Discontinuous Scheme for Solving Neutron Transport Equation in Heterogeneous Slabs

This study aims to develop positivity-preserving techniques to solve the steady neutron transport equation for a heterogeneous planar slab. Positivity-preserving properties are important and challenging issues. In particular, in regions where both the total cross section and the source-free are zero, the linear scaling limiter may be invalid when the “worst” cases, that is, both the cell average and the cell edge fluxes may be negative in the linear discontinuous (LD) method. This study aims to develop positivity-preserving techniques to solve the steady neutron transport equation for a heterogeneous planar slab. To cope with the “worst” situation, we use a modification to the linear scaling limiter by selecting the inflow or average in the adjacent cell to define the limiter factor, called “inflow preferred” and “average preferred.” These limiters maintain the accuracy of the original polynomial. Numerical results are provided to solve the Reed-like problem to verify the efficiency of the proposed schemes and to compare them with other positivity-preserving techniques.