Low Dissipative Entropic Lattice Boltzmann Method

In the entropic lattice Boltzmann approach, the stability properties are governed by the parameter α, which in turn affects the viscosity of a flow. The variation of this parameter allows one to guarantee the fulfillment of the discrete H-theorem for all spatial nodes. In the ideal case, the alteration of α from its normal value in the conventional lattice Boltzmann method (α=2) should be as small as possible. In the present work, the problem of the evaluation of α securing the H-theorem and having an average value close to α=2 is addressed. The main idea is to approximate the H-function by a quadratic function on the parameter α around α=2. The entropy balance requirement leads to a closed form expression for α depending on the values of the H-function and its derivatives. To validate the proposed method, several benchmark problems are considered: the Sod shock tube, the propagation of shear, acoustic waves, and doubly shear layer. It is demonstrated that the obtained formula for α yields solutions that show very small excessive dissipation. The simulation results are also compared with the essentially entropic and Zhao–Yong lattice Boltzmann approaches.