Reply to "Comment on 'Numerics of the lattice Boltzmann method: Effects of collision models on the lattice Boltzmann simulations'".

This Reply addresses two issues raised in the Comment [Phys. Rev. E 84, 068701 (2011)] by Karlin, Succi, and Chikatamarla (KSC): (1) A lattice Boltzmann (LB) model, which is claimed to have an H theorem, is not qualified to be called an entropic lattice Boltzmann equation (ELBE); and (2) the real ELBE with a variable relaxation time performs exceedingly well, as exhibited by their simulations of decaying "Kida vortex" flow in a three-dimensional periodic cube free of no-slip boundary. The first issue is a semantic one. We note that it was Karlin, Succi, and others who "prove the H theorem for lattice Bhatnagar-Gross-Krook models," which is the model we called ELBE in our original study to distinguish it from the usual lattice BGK model without the H theorem. Regardless of how this model is named, it does not affect the results and conclusions of our study in any way. Second, the focus of our original study is to quantify the errors of various LB models near no-slip boundaries. Hence, KSC's example, which is free of no-slip boundaries, is not relevant to our study. The results in our original paper are valid and its conclusions remain unchallenged. On the other hand, KSC's assertion that their real ELBE "provides a reliable subgrid simulation" of turbulence is not substantiated.