Extended Lattice Boltzmann Model

TL;DR

This paper introduces an extended lattice Boltzmann model that improves accuracy for high-velocity and high-temperature fluid simulations by restoring Galilean invariance and isotropy, validated through multiple benchmark problems.

Contribution

The paper presents a unified extended equilibrium formulation that enhances lattice Boltzmann models for broader and more accurate fluid dynamics simulations.

Findings

Restores Galilean invariance and isotropy in the stress tensor.

Enables simulations at higher flow velocities and temperatures.

Validated with benchmark problems including turbulence and boundary layers.

Abstract

Conventional lattice Boltzmann models for the simulation of fluid dynamics are restricted by an error in the stress tensor that is negligible only for vanishing flow velocity and at a singular value of the temperature. To that end, we propose a unified formulation that restores Galilean invariance and isotropy of the stress tensor by introducing an extended equilibrium. This modification extends lattice Boltzmann models to simulations with higher values of the flow velocity and can be used at temperatures that are higher than the lattice reference temperature, which enhances computational efficiency by decreasing the number of required time steps. Furthermore, the extended model remains valid also for stretched lattices, which are useful when flow gradients are predominant in one direction. The model is validated by simulations of two- and three-dimensional benchmark problems, including the double shear layer flow, the decay of homogeneous isotropic turbulence, the laminar boundary layer over a flat plate and the turbulent channel flow.