# Comparison between isothermal collision-streaming and finite-difference lattice Boltzmann models

## TL;DR

This paper compares two lattice Boltzmann models—collision-streaming and finite-difference—by deriving formulas to relate their results across benchmark fluid dynamics problems, highlighting their differences and similarities.

## Contribution

It provides a systematic derivation of formulas to compare collision-streaming and finite-difference LB models for physical accuracy across key benchmarks.

## Key findings

- Physical results can be related despite different complexities
- Formulas enable direct comparison of simulation outcomes
- Both models effectively simulate benchmark problems

## Abstract

We present here a comparison between collision-streaming and finite-difference lattice Boltzmann (LB) models. This study provides a derivation of useful formulae which help one to properly compare the simulation results obtained with both LB models. We consider three physical problems: the shock wave propagation, the damping of shear waves, and the decay of Taylor-Green vortices, often used as benchmark tests. Despite the different mathematical and computational complexity of the two methods, we show how the physical results can be related to obtain relevant quantities.