Second-order response matrix solution for 1D Poiseuille plane-channel flow

With increasing miniaturization of diagnostic medical devices for more effective detection of blood-borne pathogens, Poiseuille molecular flow in microchannels has become increasingly important in medical device design. Because continuum mechanics no longer applies when the Knudson number is close to or larger than unity, kinetic theory is required to precisely capture the microscopic molecular scattering responsible for molecular flow that creates a velocity profile across the channel in the flow direction. Here, we apply a response matrix solution to the 1D Poiseuille flow equation assuming a BGK scattering approximation featuring simplicity with extreme precision by following a consistent mathematical/numerical formulation leading to 8-place (9-digit) benchmarks.