Stability and multiscale analysis of an advective lattice Boltzmann scheme

In this paper we consider a two-population lattice Boltzmann algorithm to approximate the advection equation. First, the stability of this model algorithm is examined. The analysis is based on the analytic computation of the spectrum pertaining to the evolution matrix. After proving a necessary stability condition, the stability of the evolution matrix is shown, which is related to the CFL-condition. We use the model algorithm to demonstrate that formal stability criteria based on a multiscale expansion may fail to predict instability