# Relaxation-rate formula for the entropic lattice Boltzmann method

## TL;DR

This paper introduces a new relaxation-rate formula for the entropic lattice Boltzmann method that ensures stability, hydrodynamic consistency, reduces computational cost, and effectively identifies regions with rapid flow changes.

## Contribution

A novel uniform relaxation-rate formula for ELBM that guarantees the discrete H-theorem, enhances efficiency, and improves detection of flow field variations.

## Key findings

- Reduces computational cost of ELBM
- Ensures discrete H-theorem at the numerical level
- Effectively marks regions with rapid flow changes

## Abstract

An elegant and uniform relaxation-rate formula is presented for the entropic lattice Boltzmann method (ELBM). The formula not only guarantees the discrete time H-theorem at numerical level but also gives full consideration to the consistency with hydrodynamics. With this novel formula, the computational cost of the ELBM is significantly reduced and the method now can be efficiently used for a broad range of hydrodynamics applications including high Renolds number flows. Moreover, we demonstrate that the grid points where flow fields change drastically are effectively marked by the formula.