@article{Cosgrove2003:JPA, author={J. A. Cosgrove and J. M. Buick and S. J. Tonge and C. G. Munro and C. A. Greated and D. M. Campbell}, title={Application of the lattice {Boltzmann} method to transition in oscillatory channel flow}, journal={Journal of Physics A: Mathematical and General}, volume={36}, number={10}, pages={2609-2620}, url={http://stacks.iop.org/0305-4470/36/2609}, year={2003}, abstract={In this study the applicability of the lattice Boltzmann method to oscillatory channel flow with a zero mean velocity has been evaluated. The model has been compared to exact analytical solutions in the laminar case ( Re $_{\δ}$ $<$ 100, where Re $_{\δ}$ is the Reynolds number based on the Stokes layer) for the Womersley parameter 1 $<$ \α $<$ 31. In this regime, there was good agreement between numerical and exact analytical solutions. The model was then applied to study the primary instability of oscillatory channel flow with a zero mean velocity. For these transitionary flows the parameters were varied in the range 400 $<$ Re $_{\δ}$ $<$ 1000 and 4 $<$ \α $<$ 16. Disturbances superimposed on the numerical solution triggered the two-dimensional primary instability. This phenomenon has not been numerically evaluated over the range of \α or Re $_{\δ}$ currently investigated. The results are consistent with quasi-steady linear stability theories and previous numerical investigations. } }