Hybrid Kinetic/Fluid numerical method for the Vlasov-Poisson-BGK equation in the diffusive scaling

TL;DR

This paper extends a hybrid kinetic/fluid numerical method to the nonlinear Vlasov-Poisson-BGK model, aiming to reduce computational costs while maintaining accuracy through dynamic domain adaptation.

Contribution

It introduces a novel extension of a hybrid method to nonlinear models, enabling efficient simulations with adaptive domain criteria.

Findings

The method effectively reduces computational cost.

Mass conservation is maintained in numerical tests.

Performance is demonstrated through numerical examples.

Abstract

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.