Entropic Lattice Boltzmann Simulation of the Flow Past Square Cylinder

TL;DR

This paper demonstrates that the entropic lattice Boltzmann method (ELBM) effectively simulates flow past a square cylinder, accurately capturing vortex shedding frequencies across a wide range of Reynolds numbers without explicit sub-grid modeling.

Contribution

The study shows ELBM can reliably simulate complex flow phenomena over a broad Reynolds number spectrum, extending its application to engineering-relevant flows.

Findings

ELBM accurately predicts vortex shedding frequency variation with Reynolds number.

ELBM captures flow behavior from low to high Reynolds numbers without sub-grid scale models.

The method extends previous simulations to more diverse flow regimes.

Abstract

Minimal Boltzmann kinetic models, such as lattice Boltzmann, are often used as an alternative to the discretization of the Navier-Stokes equations for hydrodynamic simulations. Recently, it was argued that modeling sub-grid scale phenomena at the kinetic level might provide an efficient tool for large scale simulations. Indeed, a particular variant of this approach, known as the entropic lattice Boltzmann method (ELBM), has shown that an efficient coarse-grained simulation of decaying turbulence is possible using these approaches. The present work investigates the efficiency of the entropic lattice Boltzmann in describing flows of engineering interest. In order to do so, we have chosen the flow past a square cylinder, which is a simple model of such flows. We will show that ELBM can quantitatively capture the variation of vortex shedding frequency as a function of Reynolds number in the low as well as the high Reynolds number regime, without any need for explicit sub-grid scale modeling. This extends the previous studies for this set-up, where experimental behavior ranging from $Re\sim O(10)$ to $Re\leq 1000$ were predicted by a single simulation algorithm.