1D Poiseuille Plane Channel Flow by Second Order Response Matrix

TL;DR

This paper presents a high-precision response matrix method for modeling 1D Poiseuille flow in microchannels using kinetic theory, addressing the limitations of continuum mechanics at small scales.

Contribution

It introduces a second-order response matrix approach for 1D Poiseuille flow with BGK approximation, achieving high accuracy and benchmark standards.

Findings

Achieved 8-decimal place benchmark accuracy

Validated the response matrix method for microchannel flow

Addressed limitations of continuum mechanics at small scales

Abstract

With increasing miniaturization of diagnostic devices for more effective detection of blood-borne pathogens for example, Poiseuille molecular flow in micro channels has become increasingly relevant. Since continuum mechanics no longer applies for Poiseuille flow when the Knudson number is near or larger than unity, kinetic theory is required to capture the microscopic molecular scattering responsible for channel molecular flow and the velocity profile across a channel. Here, we apply a response matrix solution to the 1D Poiseuille flow with a BGK approximation featuring simplicity with precision by following a consistent numerical formulation leading to high precision, 8-place benchmarks.