Low Dissipative Entropic Lattice Boltzmann Method

Abstract

In the entropic lattice Boltzmann approach, the stability properties are governed by the parameter (Formula presented.), 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 (Formula presented.) from its normal value in the conventional lattice Boltzmann method ((Formula presented.)) should be as small as possible. In the present work, the problem of the evaluation of (Formula presented.) securing the H-theorem and having an average value close to (Formula presented.) is addressed. The main idea is to approximate the H-function by a quadratic function on the parameter (Formula presented.) around (Formula presented.). The entropy balance requirement leads to a closed form expression for (Formula presented.) 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 (Formula presented.) yields solutions that show very small excessive dissipation. The simulation results are also compared with the essentially entropic and Zhao–Yong lattice Boltzmann approaches.