A modified secant method for entropic lattice Boltzmann equations

Stability of lattice Boltzmann equations is governed by a parameter that is responsible for the relaxation time of the nonequilibrium system which, in turn, affects the viscosity of the flow under examination. In the entropic approach, the relaxation time is evaluated from the entropy balance equation in such a way that the entropy does not decrease at each time and spatial point. In this paper, a technique for solving the entropy balance equation using a modified secant method is proposed. It is shown that this approach provides high accuracy. As an application of the proposed method, numerical solutions of the two-dimensional double shear problem are considered. The simulation results are compared with the results obtained by other entropic methods.