A bi-fidelity method for the uncertain Vlasov-Poisson system near quasineutrality in an asymptotic-preserving particle-in-cell framework
This addresses computational challenges in plasma physics simulations for researchers, but it is incremental as it builds on prior reformulation ideas and extends them to nonlinear cases with uncertainty.
The paper tackles the Vlasov-Poisson system with massless electrons near quasineutrality and uncertainties by developing an asymptotic-preserving particle-in-cell method for deterministic cases and a bi-fidelity method for uncertainty quantification, demonstrating effectiveness through numerical experiments.
In this paper, we study the Vlasov-Poisson system with massless electrons (VPME) near quasineutrality and with uncertainties. Based on the idea of reformulation on the Poisson equation by [P. Degond et.al., $\textit{Journal of Computational Physics}$, 229 (16), 2010, pp. 5630--5652], we first consider the deterministic problem and develop an efficient asymptotic-preserving particle-in-cell (AP-PIC) method to capture the quasineutral limit numerically, without resolving the discretizations subject to the small Debye length in plasma. The main challenge and difference compared to previous related works is that we consider the nonlinear Poisson in the VPME system which contains $e^Ï$ (with $Ï$ being the electric potential) and provide an explicit scheme. In the second part, we extend to study the uncertainty quantification (UQ) problem and develop an efficient bi-fidelity method for solving the VPME system with multidimensional random parameters, by choosing the Euler-Poisson equation as the low-fidelity model. Several numerical experiments are shown to demonstrate the asymptotic-preserving property of our deterministic solver and the effectiveness of our bi-fidelity method for solving the model with random uncertainties.