Lattice operators from discrete hydrodynamics

TL;DR

This paper introduces a systematic method to derive isotropic and accurate lattice differential operators from discrete velocities in lattice hydrodynamics, enhancing computational physics simulations.

Contribution

It presents a novel scheme to obtain lattice differential operators with built-in isotropy and higher convergence order, applicable across various computational physics problems.

Findings

Provides a recursive technique for higher-order accuracy

Ensures isotropy in lattice differential operators

Applicable to a broad range of computational physics problems

Abstract

We present a general scheme to derive lattice differential operators from the discrete velocities and associated Maxwell-Boltzmann distributions used in lattice hydrodynamics. Such discretizations offer built-in isotropy and recursive techniques to increase the convergence order. This provides a simple and elegant procedure to derive isotropic and accurate discretizations of differential operators, which are expected to apply across a broad range of problems in computational physics.