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：本文简要介绍了对扩散尺度下线性碰撞动力学方程的混合模型自适应方法（参见T.~Laidin, 《arXiv 2202.03696》, 2022）向非线性平均场Vlasov-Poisson-BGK模型的扩展。该方法的目的是通过利用渐近模型较低维度的优势来降低计算成本，同时减小总体误差。其核心基于两个由扰动方法驱动的准则，以实现动态区域自适应。通过数值算例展示了该方法的性能及质量守恒特性。