Relative entropy based breakdown criteria for hybrid discrete velocity Bhatnagar–Gross–Krook and lattice Boltzmann method

Abstract

In the present paper, novel breakdown criteria for the assessment of the validity of the continuum-fluid approximation are proposed. The approach is based on relative entropy (Kullback–Leibler divergence). The considered variants of the Kullback–Leibler divergence assess the contribution of non-hydrodynamic components of the gas velocity distribution function to the overall entropy. In addition, the chi-square statistic is introduced as a breakdown variable. As benchmark problems, the plane Couette and force driven Poiseuille flows are considered for various Knudsen and Mach numbers. The modeling is performed with the difference scheme for the kinetic Bhatnagar–Gross–Krook equation and the hybrid approach: the Bhatnagar–Gross–Krook equation is applied in non-equilibrium regions, and the lattice Boltzmann method is applied as the continuum-fluid method. The simulation results show that the proposed criteria can efficiently separate equilibrium and non-equilibrium domains.