Realizability-preserving DG-IMEX method for the two-moment model of fermion transport
Realizability-preserving DG-IMEX method for the two-moment model of fermion transport
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DOI：
10.1016/j.jcp.2019.03.037
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发表时间：
2018-09
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影响因子：
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通讯作者：
Ran Chu;E. Endeve;C. Hauck;A. Mezzacappa
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文献类型：
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作者：
Ran Chu;E. Endeve;C. Hauck;A. Mezzacappa
在Zhang & Shu[1]，[2]的框架上，我们开发了一种保持可实现性的方法来模拟粒子（费米子）通过背景材料的输运，该方法使用两矩模型来演变相空间分布函数f的角矩。两矩模型使用代数矩闭包封闭；例如，由Cernohorsky & Bludman[3]和Banach & Larecki[3]提出。该模型的变体最近被用于模拟核天体物理应用中的中微子传输，包括核心坍缩超新星和紧凑的双星合并。我们采用不连续伽辽金（DG）方法进行空间离散化（部分是为了捕捉模型的渐近扩散极限），结合隐式-显式（IMEX）时间积分，稳定地跳过由粒子与背景之间频繁相互作用引起的短时间尺度。根据泡利不相容原理，需要有一个有界的分布函数（即f∈[0,1]），为了确保该方法在演化矩（粒子密度和通量）上保持严格的代数界，我们采取了适当的措施。该方案结合了一个合适的CFL条件、一个可实现约束、一个基于Fermi-Dirac统计的闭包过程和一个IMEX方案，该方案的阶段可以写成前向欧拉步和后向欧拉步的凸组合。IMEX格式形式上只有一阶精确，但在扩散极限下工作良好，并且在不与背景相互作用的情况下，简化为Shu & Osher[5]的最优二阶强保稳定显式Runge-Kutta格式。数值结果表明该方案具有保持可实现性。我们还证明，使用非基于费米-狄拉克统计的代数矩闭包可以在费米子输运的背景下导致非物理矩。
Building on the framework of Zhang & Shu [1],[2], we develop a realizability-preserving method to simulate the transport of particles (fermions) through a background material using a two-moment model that evolves the angular moments of a phase space distribution function f. The two-moment model is closed using algebraic moment closures; eg, as proposed by Cernohorsky & Bludman [3] and Banach & Larecki [4]. Variations of this model have recently been used to simulate neutrino transport in nuclear astrophysics applications, including core-collapse supernovae and compact binary mergers. We employ the discontinuous Galerkin (DG) method for spatial discretization (in part to capture the asymptotic diffusion limit of the model) combined with implicit-explicit (IMEX) time integration to stably bypass short timescales induced by frequent interactions between particles and the background. Appropriate care is taken to ensure the method preserves strict algebraic bounds on the evolved moments (particle density and flux) as dictated by Pauli's exclusion principle, which demands a bounded distribution function (ie, f∈[0, 1]). This realizability-preserving scheme combines a suitable CFL condition, a realizability-enforcing limiter, a closure procedure based on Fermi-Dirac statistics, and an IMEX scheme whose stages can be written as a convex combination of forward Euler steps combined with a backward Euler step. The IMEX scheme is formally only first-order accurate, but works well in the diffusion limit, and—without interactions with the background—reduces to the optimal second-order strong stability-preserving explicit Runge-Kutta scheme of Shu & Osher [5]. Numerical results demonstrate the realizability-preserving properties of the scheme. We also demonstrate that the use of algebraic moment closures not based on Fermi-Dirac statistics can lead to unphysical moments in the context of fermion transport.