An advanced ALE-mixed finite element method for a cardiovascular fluid–structure interaction problem with multiple moving interfaces

Abstract An advanced arbitrary Lagrangian–Eulerian (ALE) mixed finite element method (FEM) is developed for a cardiovascular fluid–structure interaction (FSI) problem with multiple moving interfaces arising from cardiovascular diseases (CVDs), where the aneurysm on the artery wall and the implanted stent graft are involved as multi-structural domains, interacting with the blood fluid in different regions through multiple moving interfaces. A monolithic, fully discrete ALE-mixed finite element method is well developed to solve the moving multi-interface problem in the cardiovascular environment, where the blood fluid region is divided into two subregions by two structural domains: the artery wall and the stent graft, inducing three moving interfaces amongst them that are interacting with each other due to the motion of the blood fluid. Consequently, a FSI-induced saddle-point linear algebraic system from the developed ALE-FEM, in which velocity variables of both the fluid and the structure are combined, together with the fluid pressure variable, is thus formed and solved by some well developed preconditioned linear solvers. Numerical experiments are carried out for a modified FSI benchmark problem and two realistic cardiovascular problems to demonstrate the effectiveness and the strength of the developed monolithic ALE-mixed finite element method. This paper is a significant extension version of the authors’ conference paper (Sun et al., 2020) [1] .