Solving Vlasov-Poisson system with an adaptive Hermite spectral method
This work provides a novel adaptive approach for solving the Vlasov-Poisson system, which is important for plasma physics simulations, but the improvements are incremental.
The paper proposes an adaptive Hermite spectral method for the Vlasov-Poisson system that uses a frequency indicator to adjust the scaling factor, enabling efficient resolution of filamentation. Numerical experiments in 1D1V and 2D2V demonstrate feasibility and efficiency.
We propose an adaptive Hermite spectral method for the Vlasov-Poisson system based on a recently developed frequency indicator that measures the contribution of the high-order expansion coefficients. Precisely, the symmetrically weighted Hermite basis with a scaling factor is utilized to approximate the distribution function to satisfy the increasing resolution requirement, which, for example, is induced by filamentation. To implement the scaling adjustment, a fast conservative projection operator is constructed in two steps. The first step is to formulate the projection as a constrained optimization problem to preserve key invariants, including mass, momentum, energy, and the $L^2$ norm of the distribution function. The second step is an ODE-based approximation developed to compute the updated expansion coefficients with linear complexity. Numerical experiments with 1D1V and 2D2V settings validate the feasibility and efficiency of this proposed adaptive Hermite method.