An interface‐tracking unified continuum model for fluid‐structure interaction with topology change and full‐friction contact with application to aortic valves

Jeannette Hiromi Spühler,Johan Hoffman

doi:10.1002/nme.6384

Abstract

SummaryAn interface tracking finite element methodology is presented for 3D turbulent flow fluid‐structure interaction, including full‐friction contact and topology changes, with specific focus on heart valve simulations. The methodology is based on a unified continuum fluid‐structure interaction model, which is a monolithic approach, where the fundamental conservation laws are formulated for the combined fluid‐structure continuum. Contact is modeled by local phase changes in the unified continuum, and computational results show the promise of the approach. The core algorithms are all based on the solution of partial differential equations with standard finite element methods, and hence any general purpose finite element library which can leverage state of the art hardware platforms can be used for the implementation of the methodology.

Highlights

1.1 Motivation1.1.1 Heart valve simulationIn the wake of medical imaging, high-performance computing, and big data, in silico medicine has emerged as a powerful tool for personalized medicine
Here we focus exclusively on the fluid-structure interaction (FSI) aspects of the simulation problem, which include the discretization of deforming structure models with contact and topology changes, coupling the structure models to fluid models such that fundamental conservation laws are respected, and the simulation of flow separation and turbulence
In previous work the unified continuum FSI (UC-FSI) model without contact has been validated for benchmark problems in both 2D48 and 3D,49 which is here complemented by a study of UC-FSI with contact for a 3D model problem under mesh refinement

Summary

Introduction

1.1 Motivation1.1.1 Heart valve simulationIn the wake of medical imaging, high-performance computing, and big data, in silico medicine has emerged as a powerful tool for personalized medicine. Patient-specific simulations have the potential to be used both in risk assessment for valve repair or replacement, for personalized clinical interventions, and for the design of prosthetic valves.[2] Quantities of interest in a heart valve simulation may be the deformation of the opening and closing valve tissue and the associated internal and surface stresses, and the blood flow dynamics including shear stress, pressure, Int J Numer Methods Eng. 2020;1–21. The equations of structure (solid) mechanics are based on a Lagrangian (material) description of the material, where each coordinate represents a material point which is tracked in time. The equations of fluid mechanics typically use an Eulerian (spatial) description, where each coordinate corresponds to a spatial point, where the flow is recorded over time. In an Arbitrary Lagrangian-Eulerian (ALE) method, the conservation laws of an FSI model are expressed with respect to an arbitrary reference coordinate system, connected to the discretization of the equations. Mesh smoothing techniques are designed to handle moderate mesh distortion without changing the mesh connectivity, while large deformations of the mesh require methods based on local or global remeshing.[11,12] For a detailed description of ALE methods see one of the several reviews available.[13]

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