Generalized finite difference method for 3-D viscous flow in stenotic tubes with large wall deformation and collapse

Abstract

A numerical method using generalized finite differences (GFD) and a three-dimensional computational model with fluid–wall interactions are introduced to investigate viscous flow in stenotic elastic tubes with large wall deformation and collapse. The computational model is based on an in vitro experimental set-up simulating artery collapse and blood flow in carotid arteries with stenoses. The Navier–Stokes equations are used as the governing equations for the fluid while a thin-shell theory is used for the wall model. Use of the unstructured GFD method and an incremental boundary iteration technique makes it possible to handle critical flow conditions with large velocity and pressure gradients and fluid–structure interactions with large deformation and wall collapse. The computational model and numerical method are validated by available analytic solutions and experimental data. Results obtained may provide useful information for early detection, prevention and diagnosis of related arterial diseases.