Duality in matrix lattice Boltzmann models

TL;DR

This paper introduces the concept of duality between hydrodynamic and kinetic variables in matrix lattice Boltzmann models, aiming to guide their design for better physical transparency and computational efficiency.

Contribution

It proposes a duality framework that informs the development of matrix lattice Boltzmann models, enhancing their physical interpretability and computational performance.

Findings

Duality concept between hydrodynamic and kinetic variables introduced

Guidelines for designing matrix lattice Boltzmann models provided

Potential improvements in model transparency and efficiency suggested

Abstract

The notion of duality between the hydrodynamic and kinetic (ghost) variables of lattice kinetic formulations of the Boltzmann equation is introduced. It is suggested that this notion can serve as a guideline in the design of matrix versions of the lattice Boltzmann equation in a physically transparent and computationally efficient way.