A computational approach for modeling flow through compliant vessels

We present a computational approach for modeling unsteady flow through compliant vessels with hyperviscoelastic wall at small to moderate fluid inertia (Re = 0.1 to 100, based on vessel radius and entering fluid velocity). Our methodology is based on a hybrid of sharp-interface (ghost-node) and diffuse-interface immersed-boundary methods for fluid/wall interaction, finite-volume/spectral method-based flow solver, and finite-element method for wall mechanics. It allows us to simulate both large inflation (nearly twice increase in vessel radius) and complex collapse (high buckling modes and irregular buckled shape) under different constitutive models (linear elastic, strain softening, strain hardening) for the wall. For the inflating vessel, comparison is presented against classical (e.g., law of Laplace) and analytical theories. At lower Re, the maximum deformation occurs near the upstream end, but with increasing Re it occurs further downstream and a recirculation region appears. For the collapsible vessel, comparison is presented against Timoshenko’s theory for multi-lobed buckled shapes, as well as the post-buckling behavior of two-lobed shapes. Constitutive models are seen to have a significant effect on the inflated shape, but not on the buckled shape.