Some Numerical Approaches to Solve Fluid Structure Interaction Problems in Blood Flow

Abstract

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.

A partitioned fully explicit Lagrangian finite element method for highly nonlinear fluid‐structure interaction problems

“…The numerical simulation of fluid‐structure interaction (FSI) problems is a topic of great relevance because of the wide range of applications in many engineering fields such as aeronautical, mechanical, civil or biomedical …”

Numerical Approach for The Evaluation of Hemodynamic Behaviour in Peripheral Arterial Disease: A Systematic Review

“…Nonetheless, numerous additional variables must be considered, including the elasticity structure of the artery wall and the stresses it endures as a result of atherosclerosis, as well as changes in material characteristics as the atherosclerotic lesion proceeds [54]. As a result, improved discretization methodologies, domain coupling techniques, and mesh interaction types are applied in fluid and solid domain problem solution using FSI [55]. Besides, FSI also important specially after interventions which permanently change local biomechanics such as stenting and bypass grafting [56,57].…”

Numerically Efficient Three-Dimensional Fluid-Structure Interaction Analysis for Composite Camber Morphing Aerostructures

“…Fluid-Structure Interaction models combine the interaction of a deformable body with the surrounding fluid flow. They are classified as either one-way or two-way routines; the former one occurs when the structural deformation affects the fluid motion-but not vice versa-whereas the latter refers to routines where both structural deformations and fluid motion affect each other [22].…”

“…On one hand, explicit algorithms (also known as loosely-coupled) consist of separate structural and aerodynamic models which are coupled and then iterated until a converge solution is achieved. On the other hand, implicit algorithms (also known as strongly-coupled) find the converged solution using a single model that simultaneously accounts for both the structure and the aerodynamics [22]. Although strongly-coupled algorithms are generally more stable, they may be difficult to program and implement as both structures and aerodynamics solvers may require significant modification to combine them in a single system of equations [23].…”

“…Eqs. (21)(22)). This circulation function enforces the shape function to have a certain value at the ζ c location, and the nature of the boundary condition is defined by the value of n. Table 1 shows different boundary conditions and their corresponding n values [19].…”