Lagrangian Entropic Lattice Boltzmann Method for Courant-Free Supersonic Compressible Flow Simulation

Traditional lattice Boltzmann methods suffer from poor stability under conditions of low viscosity, high velocity, and high temperature, accompanied by rapidly increasing memory requirements. This work introduces a novel framework for simulating highly compressible flows, namely the Lagrangian entropic lattice Boltzmann method (LELBM). The present model employed a regularized central moment collision method to ensure accurate resolution of shear viscosity, bulk viscosity, and thermal conductivity. To transcend the limitations of fixed velocity stencils, Lagrangian acoustic stencils is introduced, an adaptive population velocity construction method that unifies preexisting concepts of multispeed and shifted lattices. Additionally, developed upon the concept from numerical equilibria, entropic population reconstruction is implemented to reconstruct post-collision populations so as to satisfy post-collision moment under arbitrary velocity stencils. Moreover, the moment streaming algorithm allowed the decoupling of fixation of populations and velocity stencils, while also reducing memory complexity from polynomial order in lattice temperature to unconditionally a constant order. Incorporation of internal degrees of freedom enabled flexible adjustment of the specific heat ratio and the bulk viscosity. The unified formulation resulted in a fully Courant-free, local scheme, stable even under strong shocks, while still maintaining explicitness in time stepping. The present model has been validated under test problems of: Sod's shock tube problem, Lax problem, Shu–Osher wave, two‐dimensional Riemann problem, oblique shock problem, double Mach reflection, supersonic flow past a cylinder, and supersonic flow past a NACA0012 airfoil. The results has shown excellent agreement with reference solutions across a wide range of problems, demonstrating both the robustness and the accuracy of the LELBM formulation.