Fluid-Structure Simulations and Benchmarking of Artery Aneurysms Under Pulsatile Blood Flow

Abstract

Abstract. In this paper Fluid-structure interaction (FSI) simulations of artery aneurysms are carried out where both the fluid flow and the hyperelastic material are incompressible. We focus on time-dependent formulations adopting a monolithic approach, where the deformation of the fluid domain is taken into account according to an Arbitrary Lagrangian Eulerian (ALE) scheme. The exact Jacobian matrix is implemented by using automatic differentiation tools. The system is modeled using a specific equation shuffling that assures an optimal pivoting. We propose to solve the resulting linearized system at each nonlinear outer iteration with a GMRES solver preconditioned by a geometric multigrid algorithm with an Additive Schwarz Method (ASM) smoother.In order to test our numerical method on possible hemodynamics applications, we describe several benchmark settings. The configurations consist of realistic artery aneurysms where hybrid meshes are employed. Both two and three-dimensional benchmarks are considered. We show numerical results for the described aneurysm geometries focusing on pulsatile inflow conditions. Parallel implementation is addressed and a case of endovascular stent implantation on a cerebral aneurysm is presented. 955Available online at www.eccomasproceedia.org Eccomas Proceedia COMPDYN (2017) 955-974

A field‐split preconditioning technique for fluid‐structure interaction problems with applications in biomechanics

“…Two 2D geometries are considered, involving a venous valve and a brain aneurysm. The AS preconditioner has already been tested on these two geometries in Aulisa et al and Calandrini and Aulisa . A brief description of the function used in the venous valve simulations is also given.…”

“…Two 3D geometries are presented, a brain aneurysm and an aortic aneurysm. The AS preconditioner has already been tested on the 3D brain aneurysm geometry in Aulisa et al…”

“…To analyze the FS preconditioner for the level subsolvers, we compare its performance with the preconditioner in Aulisa et al, which is of pure domain decomposition type. In Aulisa et al and Calandrini et al, the Krylov solver in Aulisa et al has been applied to solve FSI problems with biomedical applications, namely, it has been used for stented cerebral aneurysm simulations in Aulisa et al and for magnetic drug targeting (MDT) procedures in Calandrini et al We intend to show that an FS approach is more suitable for biomedical FSI problems, where a Krylov solver preconditioned with a multigrid method is adopted.…”

“…In Richter, 44 GMG is used as a preconditioner for GMRES as we do, but for the smoothing strategy, a partitioned iteration is used based on the idea provided in van Brummelen et al 45 For an overview of some of the most popular methodologies to solve numerically the haemodynamic FSI systems, please refer to the introduction in Crosetto, 46 where a class of block triangular preconditioners is described, obtained by exploiting the block-structure of the FSI linear system.To analyze the FS preconditioner for the level subsolvers, we compare its performance with the preconditioner in Aulisa et al, 47 which is of pure domain decomposition type. In Aulisa et al 48,49 and Calandrini et al,50 the Krylov solver in Aulisa et al 47 has been applied to solve FSI problems with biomedical applications, namely, it has been used for stented cerebral aneurysm simulations in Aulisa et al 48,49 and for magnetic drug targeting (MDT) procedures in Calandrini et al 50 We intend to show that an FS approach is more suitable for biomedical FSI problems, where a Krylov solver preconditioned with a multigrid method is adopted.The biomedical applications considered for the tests include aneurysm and venous valve geometries. Both 2D and 3D simulations are carried out.…”

Fluid‐structure interaction simulations of venous valves: A monolithic ALE method for large structural displacements

“…A validation of the FSI model and solver throughout a series of 2D and three‐dimensional (3D) benchmark tests can be found in Aulisa et al, where the results obtained were compared with several existing FSI models and solvers . Previous applications of our FSI model and solver to hemodynamics problems can be found in Aulisa et al and Calandrini et al Before discussing the formulation of the problem, we introduce some notations.…”