title: Investigation of an entropic stabilizer for the lattice-Boltzmann method.
abstract: The lattice-Boltzmann (LB) method is commonly used for the simulation of fluid flows at the hydrodynamic level of description. Due to its kinetic theory origins, the standard LB schemes carry more degrees of freedom than strictly needed, e.g., for the approximation of solutions to the Navier-stokes equation. In particular, there is freedom in the details of the so-called collision operator. This aspect was recently utilized when an entropic stabilizer, based on the principle of maximizing local entropy, was proposed for the LB method [I. V. Karlin, F. Bösch, and S. S. Chikatamarla, Phys. Rev. E 90, 031302(R) (2014)]. The proposed stabilizer can be considered as an add-on or extension to basic LB schemes. Here the entropic stabilizer is investigated numerically using the perturbed double periodic shear layer flow as a benchmark case. The investigation is carried out by comparing numerical results obtained with six distinct LB schemes. The main observation is that the unbounded, and not explicitly controllable, relaxation time for the higher-order moments will directly influence the leading-order error terms. As a consequence, the order of accuracy and, in general, the numerical behavior of LB schemes are substantially altered. Hence, in addition to systematic numerical validation, more detailed theoretical analysis of the entropic stabilizer is still required in order to properly understand its properties.
authors.affiliation: Department of Physics, University of Jyväskylä, P.O. Box 35 (YFL), FI-40014 Jyväskylä, Finland and Department of Physics, Tampere University of Technology, P.O. Box 692, FI-33101 Tampere, Finland.
authors.forename: Keijo K
authors.initials: KK
authors.lastname: Mattila
authors.affiliation: Department of Petroleum Engineering, State University of Santa Catarina, 88330-668 Balneário Camboriú, Santa Catarina, Brazil.
authors.forename: Luiz A
authors.initials: LA
authors.lastname: Hegele
authors.affiliation: Mechanical Engineering Department, Federal University of Santa Catarina, 88040-900 Florianópolis, Santa Catarina, Brazil.
authors.forename: Paulo C
authors.initials: PC
authors.lastname: Philippi