Abstract We develop a conservative configuration- and velocity-space (i.e., phase-space) moving-grid strategy for the Vlasov–Fokker–Planck (VFP) equation in a planar geometry. The velocity-space grid is normalized and shifted in terms of the thermal speed and the bulk-fluid velocity, respectively. The configuration-space grid is moved according to a mesh-motion-partial-differential equation (MMPDE), which equidistributes a monitor function that is inversely proportional to the gradient-length scales of the macroscopic plasma quantities. The resulting inertial terms in the transformed VFP equations are discretized to ensure the discrete conservation of mass, momentum, and energy. To satisfy the discrete conservation theorems in the presence of phase-space mesh motion, we employ the method of discrete nonlinear constraints – explored in previous studies – but the underlying symmetries are determined in a much more efficient manner than before. The conservative grid-adaptivity strategy provides an efficient scheme that resolves important physical structures in the phase-space while controlling the computational complexity at all times. We demonstrate the favorable features of the proposed algorithm through a set of test cases of increasing complexity. The problems test independent components of the algorithms, as well as the integrated capability on settings relevant to inertial confinement fusion.

中文翻译：

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1D-2V Vlasov–Fokker–Planck 求解器的保守相空间移动网格策略

摘要 我们为平面几何中的 Vlasov-Fokker-Planck (VFP) 方程开发了一种保守的配置和速度空间（即相空间）移动网格策略。速度空间网格分别根据热速度和体积流体速度进行归一化和移动。配置空间网格根据网格运动偏微分方程 (MMPDE) 移动，该方程均衡分布与宏观等离子体量的梯度长度尺度成反比的监测函数。转换后的 VFP 方程中产生的惯性项被离散化，以确保质量、动量和能量的离散守恒。为了满足存在相空间网格运动的离散守恒定理，我们采用离散非线性约束的方法——在之前的研究中探索过——但潜在的对称性是以比以前更有效的方式确定的。保守的网格自适应策略提供了一种有效的方案，可以在始终控制计算复杂性的同时解决相空间中的重要物理结构。我们通过一组越来越复杂的测试用例来证明所提出算法的有利特征。这些问题测试算法的独立组件，以及与惯性约束融合相关的设置的集成能力。保守的网格自适应策略提供了一种有效的方案，可以在始终控制计算复杂性的同时解决相空间中的重要物理结构。我们通过一组越来越复杂的测试用例来证明所提出算法的有利特征。这些问题测试算法的独立组件，以及与惯性约束融合相关的设置的集成能力。保守的网格自适应策略提供了一种有效的方案，可以在始终控制计算复杂性的同时解决相空间中的重要物理结构。我们通过一组越来越复杂的测试用例来证明所提出算法的有利特征。这些问题测试算法的独立组件，以及与惯性约束融合相关的设置的集成能力。