We present a numerical algorithm that enables a phase-space adaptive Eulerian Vlasov–Fokker–Planck (VFP) simulation of inertial confinement fusion (ICF) capsule implosions. 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.

我们提出了一种数值算法，可以实现惯性约束聚变（ICF）胶囊内爆的相空间自适应欧拉夫·弗拉索夫·福克·普朗克（VFP）仿真。该方法依赖于将最近的质量，动量和节能的相空间移动网格自适应策略扩展到球形几何形状。在配置空间中，我们采用了网格运动偏微分方程（MMPDE）策略，而在速度空间中，网格随着等离子的演化温度和漂移速度而扩展/收缩和移动。通过转换基本的VFP方程来处理网格运动转换为计算（逻辑）坐标，并仔细离散化所得的惯性项以确保守恒。为了解决球形内爆系统中时空变化的动力学问题，我们为配置空间中的MMPDE开发了一种新颖的非线性稳定策略。该策略依赖于非线性优化程序，该程序在网格质量和网格体积变化率之间进行优化，以确保解决方案的准确性和稳定性。内爆ICF胶囊的数量受几个边界条件驱动：（1）弹性移动壁边界；（2）时间相关的麦克斯韦狄利克雷边界；（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对我们来说是新的。我们通过一系列测试问题（包括Guderley和Van-Dyke内爆问题）验证了我们策略的实施，这是有史以来首次使用Vlasov-Fokker-Planck模型报道的问题。