A recently introduced family of lattice Boltzmann (LB) models (Karlin,
B\"osch, Chikatamarla, Phys. Rev. E, 2014) is studied in detail for
incompressible two-dimensional flows. A framework for developing LB models
based on entropy considerations is laid out extensively. Second order rate of
convergence is numerically confirmed and it is demonstrated that these entropy
based models recover the Navier-Stokes solution in the hydrodynamic limit.
Comparison with the standard Bhatnagar-Gross-Krook (LBGK) and the entropic
lattice Boltzmann method (ELBM) demonstrates the superior stability and
accuracy for several benchmark flows and a range of grid resolutions and
Reynolds numbers. High Reynolds number regimes are investigated through the
simulation of two-dimensional turbulence, particularly for under-resolved
cases. Compared to resolved LBGK simulations, the presented class of LB models
demonstrate excellent performance and capture the turbulence statistics with
good accuracy.Comment: To be published in Proceedings of Discrete Simulation of Fluid
Dynamics DSFD 201
