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.

翻译：矩模型通过合适的封闭策略能够构建精确且计算高效的粒子输运求解器。为此，我们针对线性输运的M1模型提出一种新的渐近保持格式，该格式对任意努森数具有均匀适用性。其核心思想是在数值层面上将M1封闭策略应用于现有针对相应动力学方程的渐近保持格式——即最初在文献[27]中提出、后经文献[24]扩展至线性输运的统一气体动力学格式（UGKS）。为确保新格式中矩的可实现性，需维持UGKS的正性特征。我们通过提出一种新型时间域密度重构方法实现该性质，同时建议并验证了二阶扩展方案。多种数值算例证明了该格式的优良性能。