An immersed fluid–structure interaction method targeted for heart valve applications

• Published in: Computer methods in applied mechanics and engineering 2025-02, Vol.435, p.117634, Article 117634
• Main Authors: Black, Ryan T., Park, George Ilhwan
• Format: Article
• Language: English
• Subjects: Fictitious domain/distributed Lagrange multiplier method; Fluid–structure interaction; Heart valve modeling; Immersed finite element method; Immersed methods; Variational multiscale method
• ISSN: 0045-7825
• DOI: 10.1016/j.cma.2024.117634

In this paper, we propose several improvements to existing fictitious domain/distributed Lagrange multiplier (FD/DLM) type immersed fluid–structure interaction (FSI) methods targeted for FSI analysis of heart valve dynamics. We utilize the variational multiscale (VMS) method to improve accuracy and robustness on under-resolved grids expected with immersed FSI techniques, as well as for the wide range of Reynolds numbers observed over the cardiac cycle. For time discretization, we use a variant of the generalized-α method that achieves second order accuracy for pressure, and present a new predictor–corrector algorithm necessary for the present approach. We focus on immersed nearly-incompressible solids, as most biological soft tissues are modeled this way. We investigate several different forms of dilatational penalty terms and various modeling assumptions that can be made for immersed nearly-incompressible solids to counteract errors that arise from weak satisfaction of the incompressibility constraint and interpolation between the fluid and overlapping solid meshes. Several test problems are considered to evaluate the proposed immersed FSI framework, including an idealized heart valve problem with heterogeneous leaflets as well as an anisotropic model for the valves.