High-order fluid–structure interaction in 2D and 3D application to blood flow in arteries

Abstract

This paper addresses the numerical approximation of fluid–structure interaction (FSI) problems through the arbitrary Lagrangian Eulerian (ALE) framework, high-order methods and a Dirichlet–Newmann approach for the coupling. The paper is divided into two main parts. The first part concerns the discretization method for the FSI problem. We introduce an improved ALE map, capable of handling curved geometries in 2D and 3D in a unified manner, that is based on a local differential operator. We also propose a minimal continuous interior penalty (CIP) stabilization term for the fluid discretization that accounts for a smaller computational effort, while stabilizing the flow regime. The second part is dedicated to validating our numerical strategy through a benchmark and some applications to blood flow in arteries.