A novel velocity discretization for lattice Boltzmann method: Application to compressible flow.

This article focuses on a novel velocity discretization method for the lattice Boltzmann method (LBM) that enables accurate recovery of the compressible Navier–Stokes equations by fully matching the equilibrium moments of the Maxwell–Boltzmann distribution up to the third order. Unlike the standard LBM, which uses delta functions for velocity discretization and fails to reproduce correct third moments—leading to error terms that break Galilean invariance and limit applicability to incompressible flows—the new approach replaces delta functions with bump functions characterized by both mean and variance. This addition provides sufficient degrees of freedom to eliminate spurious error terms without significantly increasing computational complexity or altering the standard LBM algorithm. The method is validated through Chapman–Enskog analysis and benchmark simulations including Poiseuille flow, sound wave decay, Couette flow with density gradients, and flow over a cylinder, demonstrating accurate viscosity measurements, restored Galilean invariance, and stable simulations at high Reynolds (∼1000) and Mach numbers (near 1).