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

TL;DR

This paper introduces a hybrid numerical method for the Vlasov-BGK equation that combines kinetic and fluid models to reduce computational costs while maintaining accuracy, especially in diffusive regimes.

Contribution

The paper develops a dynamic domain decomposition approach based on two criteria to efficiently couple kinetic and fluid models in solving the Vlasov-BGK equation.

Findings

The hybrid method is significantly more efficient than full kinetic simulations.

The method conserves mass effectively.

Properties like accuracy and stability are analyzed.

Abstract

This paper presents a hybrid numerical method for linear collisional kinetic equations with diffusive scaling. The aim of the method is to reduce the computational cost of kinetic equations by taking advantage of the lower dimensionality of the asymptotic fluid model while reducing the error induced by the latter approach. It relies on two criteria motivated by a pertubative approach to obtain a dynamic domain decomposition. The first criterion quantifies how far from a local equilibrium in velocity the distribution function of particles is. The second one depends only on the macroscopic quantities that are available on the whole computing domain. Interface conditions are dealt with using a micro-macro decomposition and the method is significantly more efficient than a standard full kinetic approach. Some properties of the hybrid method are also investigated, such as the conservation of mass.