Luo Li-Shi
Department of Mathematics & Statistics and Center for Computational Sciences, Old Dominion University, Norfolk, Virginia 23529, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Oct;86(4 Pt 2):048701. doi: 10.1103/PhysRevE.86.048701. Epub 2012 Oct 8.
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.
本回复针对卡林、苏奇和奇卡塔马拉（KSC）在评论文章[《物理评论E》84, 068701 (2011)]中提出的两个问题：（1）一个声称具有H定理的格子玻尔兹曼（LB）模型，没有资格被称为熵格子玻尔兹曼方程（ELBE）；（2）具有可变弛豫时间的真实ELBE表现得非常好，如他们在无滑移边界的三维周期性立方体中对衰减的“木田涡旋”流的模拟所示。第一个问题是语义问题。我们注意到，是卡林、苏奇等人“证明了格子 Bhatnagar-Gross-Krook模型的H定理”，这就是我们在最初研究中称为ELBE的模型，以将其与没有H定理的普通格子BGK模型区分开来。无论该模型如何命名，都不会以任何方式影响我们研究的结果和结论。其次，我们最初研究的重点是量化各种LB模型在无滑移边界附近的误差。因此，KSC的无无滑移边界的例子与我们的研究无关。我们原论文中的结果是有效的，其结论仍然没有受到挑战。另一方面，KSC声称他们的真实ELBE“为湍流提供了可靠的亚格子模拟”这一说法没有依据。
