Immersogeometric Analysis of Bioprosthetic Heart Valves, Using the Dynamic Augmented Lagrangian Method

Abstract

In the mid-2010s, we began applying a combination of isogeometric analysis and immersed boundary methods to the problem of bioprosthetic heart valve (BHV) fluid–structure interaction (FSI). This chapter reviews how our research on BHV FSI (1) crystallized the emerging concept of immersogeometric analysis, (2) introduced a new semi-implicit numerical method for weakly enforcing constraints in time dependent problems, which we refer to as the dynamic augmented Lagrangian approach, and (3) clarified the important role of mass conservation in immersed FSI analysis. We illustrate these contributions with selected numerical results and discuss future improvements to, and applications of, the computational FSI techniques we have developed.