Maximum Entropy Boundaries in Lattice Boltzmann Method

Vasili Baranau1 1. Department of Chemistry, Philipps-Universität Marburg, Hans-Meerwein-Strasse, 35032 Marburg, Germany Corresponding author: Vasili Baranau, [email protected] Abstract: We propose a universal approach in the framework of the lattice Boltzmann method (LBM) to modeling constant velocity constraints and constant temperature constraints on curved walls, which doesn’t depend on dimensionality, LBM scheme, boundary geometry; which is numerically stable, accurate and local and has a good physical background. This technique, called a maximum entropy method, utilizes the idea of recovering unknown populations on boundary nodes through minimizing node state deviation from equilibrium while assuring velocity or temperature restrictions. Also, theoretical justifications of a popular Zou-He boundaries technique and isothermal boundaries algorithm are provided on the basis of the method derived. Finally, while conducting numerical benchmarks, typical straight boundaries algorithm (Zou-He) was compared to a typical curved boundaries algorithm (Guo-Zheng).