Entropic Multi-Relaxation Models for Simulation of Fluid Turbulence

TL;DR

This paper analyzes a family of entropy-based lattice Boltzmann models for simulating 2D fluid turbulence, demonstrating their stability, accuracy, and effectiveness in high Reynolds number regimes compared to traditional methods.

Contribution

It provides a detailed framework for entropy-based LB models, confirms their second-order convergence, and shows their superior performance in turbulence simulations over existing models.

Findings

Models recover Navier-Stokes solutions in the hydrodynamic limit.

Entropy-based LB models outperform LBGK and ELBM in stability and accuracy.

Effective in simulating high Reynolds number turbulence, especially in under-resolved cases.

Abstract

A recently introduced family of lattice Boltzmann (LB) models (Karlin, B\"osch, Chikatamarla, Phys. Rev. E, 2014) is studied in detail for incompressible two-dimensional flows. A framework for developing LB models based on entropy considerations is laid out extensively. Second order rate of convergence is numerically confirmed and it is demonstrated that these entropy based models recover the Navier-Stokes solution in the hydrodynamic limit. Comparison with the standard Bhatnagar-Gross-Krook (LBGK) and the entropic lattice Boltzmann method (ELBM) demonstrates the superior stability and accuracy for several benchmark flows and a range of grid resolutions and Reynolds numbers. High Reynolds number regimes are investigated through the simulation of two-dimensional turbulence, particularly for under-resolved cases. Compared to resolved LBGK simulations, the presented class of LB models demonstrate excellent performance and capture the turbulence statistics with good accuracy.