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

Kamensky, David
Hsu, Ming-Chen
Hsu, Ming-Chen
Yu, Yue
Evans, John
Sacks, Michael
Hughes, Thomas
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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.

<p>This is a manuscript of an article published as Kamensky, David, Ming-Chen Hsu, Yue Yu, John A. Evans, Michael S. Sacks, and Thomas JR Hughes. "Immersogeometric cardiovascular fluid–structure interaction analysis with divergence-conforming B-splines." Computer Methods in Applied Mechanics and Engineering 314 (2017): 408-472. doi: <a href="" target="_blank">10.1016/j.cma.2016.07.028</a>. Posted with permission.</p>
Fluid–structure interaction, Bioprosthetic heart valve, Immersogeometric analysis, Isogeometric analysis, Divergence-conforming B-splines, Immersed boundary method