  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.
