Lagrangian entropic lattice Boltzmann method for Courant-free supersonic compressible flow simulation

Abstract: This work presents the Lagrangian entropic lattice Boltzmann method (LELBM), a novel framework for supersonic lattice Boltzmann method that surpasses traditional restrictions on velocity, temperature, viscosity, and memory, resulting in stable and efficient Courant-free LBM formulation, while still maintaining explicit time stepping. A regularized central moment collision method coupled with a double-distribution function (DDF) that considers internal degrees of freedom enabled the precise control of shear viscosity, bulk viscosity, and thermal conductivity. Lagrangian acoustic stencils (LAS), a generalized multispeed shifted lattice construction method, is introduced to adapt to arbitrary local velocity and temperature. Additionally, entropic population reconstruction (EPR) has been used to obtain entropy-satisfying post-collision population while achieving both positivity and conservation of moments. Memory requirements are drastically reduced from a polynomial order of temperature to a constant by employing moment streaming (MS) algorithm. The unified LELBM framework is validated through comprehensive benchmark problems. In one dimension, the model is evaluated through Sod's shock tube, Lax problem, and Shu-Osher wave. In two dimensions, 2D Riemann problem, double Mach reflection, oblique shock, supersonic flow past a circular cylinder, and supersonic flow past a NACA0012 airfoil have been tested to assess the robustness and accuracy of the proposed algorithm.