This short note presents an extension of the hybrid, model-adaptation method introduced in [T.~Laidin, \textit{arXiv 2202.03696}, 2022] for linear collisional kinetic equations in a diffusive scaling to the nonlinear mean-field Vlasov-Poisson-BGK model. The aim of the approach is to reduce the computational cost by taking advantage of the lower dimensionality of the asymptotic model while reducing the overall error. It relies on two criteria motivated by a perturbative approach to obtain a dynamic domain adaptation. The performance of the method and the conservation of mass are illustrated through numerical examples.

翻译：本文简报将文献[T. Laidin, 《arXiv 2202.03696》, 2022]中针对扩散标度下线性碰撞动力学方程提出的混合模型自适应方法，拓展至非线性平均场Vlasov-Poisson-BGK模型。该方法旨在利用渐近模型的低维特性降低计算成本，同时减小整体误差。其核心基于微扰方法推导的两个判据，实现动态区域自适应适配。数值算例验证了方法的性能与质量守恒特性。