The lattice Boltzmann method is increasingly important in facilitating large-scale fluid dynamics simulations. To date, these simulations have been built on discretized velocity models of up to 27 neighbors. Recent work has shown that higher order approximations of the continuum Boltzmann equation enable not only recovery of the Navier-Stokes hydro-dynamics, but also simulations for a wider range of Knudsen numbers, which is especially important in micro- and nano-scale flows. These higher-order models have significant impact on both the communication and computational complexity of the application. We present a performance study of the higher-order models as compared to the traditional ones, on both the IBM Blue Gene/P and Blue Gene/Q architectures. We study the tradeoffs of many optimizations methods such as the use of deep halo level ghost cells that, alongside hybrid programming models, reduce the impact of extended models and enable efficient modeling of extreme regimes of computational fluid dynamics. © 2013 IEEE.