Immersogeometric cardiovascular fluid–structure interaction analysis with divergence-conforming B-splines

• Published in: Computer methods in applied mechanics and engineering Vol. 314; pp. 408 - 472
• Main Authors: Kamensky, David, Hsu, Ming-Chen, Yu, Yue, Evans, John A., Sacks, Michael S., Hughes, Thomas J.R.
• Format: Journal Article
• Language: English
• Published: Netherlands Elsevier B.V 01-02-2017; Elsevier BV
• Subjects: Bioprosthetic heart valve; Computation; Conservation; Discretization; Divergence; Divergence-conforming B-splines; Fluid-structure interaction; Heart; Heart valves; Immersed boundary method; Immersogeometric analysis; In vitro methods and tests; Isogeometric analysis; Leakage; Pumps; Splines; Isogeometric analysis; Fluid–structure interaction; Divergence-conforming B-splines; Bioprosthetic heart valve; Immersed boundary method; Immersogeometric analysis
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2016.07.028

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 an in vitro experiment that pumps water through an artificial valve.
•Div-conforming B-splines improve immersed fluid–structure interaction (FSI) analysis.•Strong mass conservation prevents spurious non-physical leakage through barriers.•Semi-implicit time integration is shown to converge a priori for a model problem.•Div-conforming immersogeometric FSI analysis is practical for heart valve analysis.•FSI simulations reproduce qualitative features of in vitro experiments.