Some numerical approaches to solve fluid structure interaction problems in blood flow are reviewed. Fluid structure interaction is the interaction between a deformable structure with either an internal or external flow. A discussion on why the compliant artery associated with fluid structure interaction should be taken into consideration in favor of the rigid wall model being included. However, only the Newtonian model of blood is assumed, while various structure models which include, amongst others, generalized string models and linearly viscoelastic Koiter shell model that give a more realistic representation of the vessel walls compared to the rigid structure are presented. Since there exists a strong added mass effect due to the comparable densities of blood and the vessel wall, the numerical approaches to overcome the added mass effect are discussed according to the partitioned and monolithic classifications, where the deficiencies of each approach are highlighted. Improved numerical methods which are more stable and offer less computational cost such as the semi-implicit, kinematic splitting, and the geometrical multiscale approach are summarized, and, finally, an appropriate structure and numerical scheme to tackle fluid structure interaction problems are proposed.
This paper discusses the effect of different geometric representations of stenosis on the numerical solution of one-dimensional unsteady blood flow in stenotic blood vessel (or stenosis) taking into account fluid-structure interaction. In the formulation, a collapsible pressure-area constitutive relation is added to the coupled mass and momentum equations to allow for the interaction between the cross sectional area, volumetric flow rate and pressure of the flow and hence the prevalence of the one-dimensional fluid-structure interaction. The formulation is stabilized by employing Streamline-Upwind Petrov-Galerkin scheme. Non-reflecting boundary conditions are imposed based on the method of characteristics. Flow characteristics and the geometrical effects of the stenosis are then discussed. Numerical results show that stenosis with irregular shape is more prone to collapse as compared to the smooth one for a given baseline conditions. This study, thus, highlights the importance of representing the shape of the stenosis as close as possible as it might give information otherwise missing in the simplistic smooth representation of the stenosis.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.