惯性约束聚变容器球形内爆的欧拉Vlasov-Fokker-Planck算法
An Eulerian Vlasov-Fokker-Planck Algorithm for Spherical Implosion Simulations of Inertial Confinement Fusion Capsules
摘要：
提出了一种数值算法，实现了惯性约束聚变（ICF）密封舱内爆的相空间自适应欧拉VFP（Eulerian Vlasov-Fokker-Planck）模拟。该方法依赖于扩展最近的质量，动量和能量守恒相空间移动网格自适应策略，球面几何。在位形空间，我们采用网格运动偏微分方程（MMPDE）的策略，而在速度空间，网格的扩展/收缩和移动的等离子体的演变温度和漂移速度。网格运动是通过将基本的VFP方程转换成计算（逻辑）坐标来处理的，由此产生的惯性项被仔细离散化以确保守恒。为了处理球内爆系统的空间和时间变化的动力学，我们提出了一种新的非线性镇定策略的MMPDE的位形空间。该策略依赖于一个非线性优化过程，优化网格质量和体积变化率之间的网格，以确保解决方案的准确性和稳定性。ICF胶囊的内爆由几个边界条件驱动：1）弹性移动壁边界; 2）时间相关的麦克斯韦Dirichlet边界;和3）压力驱动的拉格朗日边界。其中，压力驱动的拉格朗日边界驱动器是新的知识。我们的策略的实施是通过一组测试问题，包括Guderley和Van-Dyke内爆问题验证-有史以来第一次报告使用Vlasov-Fokker-Planck模型。
英文摘要：
We present a numerical algorithm that enables a phase-space adaptive Eulerian Vlasov-Fokker-Planck (VFP) simulation of an inertial confinement fusion (ICF) capsule implosion. The approach relies on extending a recent mass, momentum, and energy conserving phase-space moving-mesh adaptivity strategy to spherical geometry. In configuration space, we employ a mesh motion partial differential equation (MMPDE) strategy while, in velocity space, the mesh is expanded/contracted and shifted with the plasma's evolving temperature and drift velocity. The mesh motion is dealt with by transforming the underlying VFP equations into a computational (logical) coordinate, with the resulting inertial terms carefully discretized to ensure conservation. To deal with the spatial and temporally varying dynamics in a spherically imploding system, we have developed a novel nonlinear stabilization strategy for MMPDE in the configuration space. The strategy relies on a nonlinear optimization procedure that optimizes between mesh quality and the volumetric rate change of the mesh to ensure both accuracy and stability of the solution. Implosions of ICF capsules are driven by several boundary conditions: 1) an elastic moving wall boundary; 2) a time-dependent Maxwellian Dirichlet boundary; and 3) a pressure-driven Lagrangian boundary. Of these, the pressure-driven Lagrangian boundary driver is new to our knowledge. The implementation of our strategy is verified through a set of test problems, including the Guderley and Van-Dyke implosion problems --the first-ever reported using a Vlasov-Fokker-Planck model.
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