An asymptotic preserving kinetic scheme for the M1 model of linear transport

Moment models with suitable closure can lead to accurate and computationally efficient solvers for particle transport. Hence, we propose a new asymptotic preserving scheme for the M1 model of linear transport that works uniformly for any Knudsen number. Our idea is to apply the M1 closure at the numerical level to an existing asymptotic preserving scheme for the corresponding kinetic equation, namely the Unified Gas Kinetic Scheme (UGKS) originally proposed in Mieussens (2013) and extended to linear transport in Xu and Huang (2010). A second order extension is suggested and validated. The generic nature of this method is also demonstrated in an application to the M2 model. Several test cases show the performances of this new scheme in both the M1 and M2 case.