  The immersed boundary (IB) method is a non-body conforming approach to
fluid-structure interaction (FSI) that uses an Eulerian description of the
momentum, viscosity, and incompressibility of a coupled fluid-structure system
and a Lagrangian description of the deformations, stresses, and resultant
forces of the immersed structure. Integral transforms with Dirac delta function
kernels couple the Eulerian and Lagrangian variables, and in practice,
discretizations of these integral transforms use regularized delta function
kernels. Many different kernel functions have been proposed, but prior
numerical work investigating the impact of the choice of kernel function on the
accuracy of the methodology has been limited. This work systematically studies
the effect of the choice of regularized delta function in several FSI benchmark
tests using the immersed finite element/difference (IFED) method, which is an
extension of the IB method that uses a finite element structural
discretizations combined with a Cartesian grid finite difference method for the
incompressible Navier-Stokes equations. The IFED formulation evaluates the
regularized delta function on a collection of interaction points that can be
chosen to be denser than the nodes of the Lagrangian mesh, and this study
investigates the effect of varying the relative mesh widths of the Lagrangian
and Eulerian discretizations. Our results indicate that kernels satisfying a
commonly imposed even-odd condition require higher resolution to achieve
similar accuracy as kernels that do not satisfy. We also find that narrower
kernels are more robust and that structural meshes that are substantially
coarser than the Cartesian grid can yield high accuracy for shear-dominated
cases but not for cases with large normal forces. We verify our results in a
large-scale FSI model of a bovine pericardial bioprosthetic heart valve in a
pulse duplicator.
