  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
[27] and extended to linear transport in [24]. In order to ensure the moments
realizability in this new scheme, the UGKS positivity needs to be maintained.
We propose a new density reconstruction in time to obtain this property. A
second order extension is also suggested and validated. Several test cases show
the performances of this new scheme.
