title: Immersogeometric cardiovascular fluid-structure interaction analysis with divergence-conforming B-splines.
abstract: This paper uses a divergence-conforming B-spline fluid discretization to address the long-standing issue of poor mass conservation in immersed methods for computational fluid-structure interaction (FSI) that represent the influence of the structure as a forcing term in the fluid subproblem. We focus, in particular, on the immersogeometric method developed in our earlier work, analyze its convergence for linear model problems, then apply it to FSI analysis of heart valves, using divergence-conforming B-splines to discretize the fluid subproblem. Poor mass conservation can manifest as effective leakage of fluid through thin solid barriers. This leakage disrupts the qualitative behavior of FSI systems such as heart valves, which exist specifically to block flow. Divergence-conforming discretizations can enforce mass conservation exactly, avoiding this problem. To demonstrate the practical utility of immersogeometric FSI analysis with divergence-conforming B-splines, we use the methods described in this paper to construct and evaluate a computational model of anin vitroexperiment that pumps water through an artificial valve.
authors.affiliation: Center for Cardiovascular Simulation, Institute for Computational Engineering and Sciences, The University of Texas at Austin, 201 East 24th St, Stop C0200, Austin, TX 78712, USA.
authors.forename: David
authors.initials: D
authors.lastname: Kamensky
authors.affiliation: Department of Mechanical Engineering, Iowa State University, 2025 Black Engineering, Ames, IA 50011, USA.
authors.forename: Ming-Chen
authors.initials: MC
authors.lastname: Hsu
authors.affiliation: Department of Mathematics, Lehigh University, Christmas-Saucon Hall, 14 E. Packer Ave, Bethlehem, PA 18015, USA.
authors.forename: Yue
authors.initials: Y
authors.lastname: Yu
authors.affiliation: Department of Aerospace Engineering Sciences, University of Colorado at Boulder, 429 UCB, Boulder, CO 80309, USA.
authors.forename: John A
authors.initials: JA
authors.lastname: Evans
authors.affiliation: Center for Cardiovascular Simulation, Institute for Computational Engineering and Sciences, The University of Texas at Austin, 201 East 24th St, Stop C0200, Austin, TX 78712, USA.
authors.forename: Michael S
authors.initials: MS
authors.lastname: Sacks
authors.affiliation: Center for Cardiovascular Simulation, Institute for Computational Engineering and Sciences, The University of Texas at Austin, 201 East 24th St, Stop C0200, Austin, TX 78712, USA.
authors.forename: Thomas J R
authors.initials: TJ
authors.lastname: Hughes
keywords: Bioprosthetic heart valve; Divergence-conforming B-splines; Fluid–structure interaction; Immersed boundary method; Immersogeometric analysis; Isogeometric analysis