We consider the solution of the fully kinetic (including electrons) Vlasov-Ampère system in a one-dimensional physical space and two-dimensional velocity space (1D-2V) for an arbitrary number of species with a time-implicit Eulerian algorithm. The problem of velocity-space meshing for disparate thermal and bulk velocities is dealt with by an adaptive coordinate transformation of the Vlasov equation for each species, which is then discretized, including the resulting inertial terms. Mass, momentum, and energy are conserved, and Gauss's law is enforced to within the nonlinear convergence tolerance of the iterative solver through a set of nonlinear constraint functions while permitting significant flexibility in choosing discretizations in time, configuration, and velocity space. We mitigate the temporal stiffness introduced by, e.g., the plasma frequency through the use of high-order/low-order (HOLO) acceleration of the iterative implicit solver. We present several numerical results for canonical problems of varying degrees of complexity, including the multiscale ion-acoustic shock wave problem, which demonstrate the efficacy, accuracy, and efficiency of the scheme.

我们考虑使用时间隐式欧拉算法，针对任意数量的物种，在一维物理空间和二维速度空间（1D-2V）中对全动力学（包括电子）的Vlasov-Ampère系统进行求解。通过对每个物种的Vlasov方程进行自适应坐标变换来处理不同的热速度和体速度的速度空间啮合问题，然后将其离散化，包括得到的惯性项。保留质量，动量和能量，并通过一组非线性约束函数将高斯定律强制执行在迭代求解器的非线性收敛容限之内，同时允许在选择时间，配置和速度空间的离散化方面具有显着的灵活性。我们减轻了例如 通过使用迭代隐式求解器的高阶/低阶（HOLO）加速来产生等离子体频率。我们针对复杂程度不同的规范问题提供了多个数值结果，包括多尺度离子声波冲击问题，这些结果证明了该方案的有效性，准确性和效率。