Poiseuille flow in curved spaces

TL;DR

This paper derives a universal flux law for Poiseuille flow in curved channels with localized metric perturbations, validated through an improved lattice Boltzmann model in curved space.

Contribution

It introduces a universal flux law for curved space Poiseuille flow and enhances the lattice Boltzmann model for better accuracy in curved geometries.

Findings

Flux depends on average metric perturbation parameters.

Derived a universal flux law for curved channels.

Validated the model with reduced lattice effects.

Abstract

We investigate Poiseuille channel flow through intrinsically curved media, equipped with localized metric perturbations. To this end, we study the flux of a fluid driven through the curved channel in dependence of the spatial deformation, characterized by the parameters of the metric perturbations (amplitude, range and density). We find that the flux depends only on a specific combination of parameters, which we identify as the average metric perturbation, and derive a universal flux law for the Poiseuille flow. For the purpose of this study, we have improved and validated our recently developed lattice Boltzmann model in curved space by considerably reducing discrete lattice effects.