Implementation and Validation of a 1D Fluid Model for Collapsible Channels

Abstract

A 1D fluid model is implemented for the purpose of fluidstructure interaction (FSI) simulations in complex and completely collapsible geometries, particularly targeting the case of obstructive sleep apnea (OSA). The fluid mechanics are solved separately from any solid mechanics, making possible the use of a highly complex and/or blackbox solver for the solid mechanics. The fluid model is temporally discretized with a secondorder scheme and spatially discretized with an asymmetrical fourthorder scheme that is robust in highly uneven geometries. A completely collapsing and reopening geometry is handled smoothly using a modified area function. The numerical implementation is tested with two drivengeometry cases: (1) an inviscid analytical solution and (2) a completely closing geometry with viscous flow. Threedimensional fluid simulations in static geometries are performed to examine the assumptions of the 1D model, and with a welldefined pressurerecovery constant the 1D model agrees well with 3D models. The model is very fast computationally, is robust, and is recommended for OSA simulations where the bulk flow pressure is primarily of interest.