AI 中文总结
本文提出用特征映射方法（CMM）模拟含碰撞的动力学等离子体，通过存储子积分处理源项，避免刚性隐式积分，在BGK和Vlasov-Poisson-BGK方程上实现三阶收敛，并展示细尺度缩放特性。
AI 中文摘要
本工作展示了使用特征映射方法（CMM）模拟含碰撞动力学等离子体的初步步骤。CMM是一种半拉格朗日方法，利用半群结构高效存储微分同胚流映射。通过半群结构，可以将各个子映射复合，将流向后关联到其初始出发点。本工作的新颖之处在于通过存储与各个子映射对应的子积分来处理源项，从而实现高效积分。此外，我们利用拉格朗日结构避免在流体力学区域进行隐式时间积分，该区域已知是刚性的。我们在Boltzmann-BGK和Vlasov-Poisson-BGK方程上对我们的方法进行基准测试，并考虑不同的测试案例：Sod激波管问题和不同Knudsen数下的非线性Landau阻尼。我们展示了三阶空间和时间收敛性，并说明了CMM对bump-on-tail不稳定性的细尺度缩放性质。
英文摘要
This work presents the first steps for simulating kinetic plasmas with collisions using the characteristic mapping method (CMM). The CMM is a semi-Lagrangian method that explores a semi-group structure to store diffeomorphic flow maps efficiently. Using the semi-group structure, individual submaps can be composed to relate the flow backward in time to its initial food point. The novelty of the presented work is handling the source term by storing sub-integrals that correspond to the individual sub-maps and allow efficient integration. Furthermore, we use the Lagrangian structure to avoid implicit time integration in the hydrodynamic regime, which is known to be stiff. We benchmark our method on the Boltzmann-BGK and Vlasov-Poisson-BGK equations and consider different test cases, the Sod shock tube problem and nonlinear Landau damping for different Knudsen numbers. We show third-order spatial and temporal convergence and illustrate the fine-scale zoom property of CMM for the bump-on-tail instability.
