Mike Lee’s paper, On the Lagrangian-Eulerian coupling in the immersed finite element/difference method, has been accepted to appear in Journal of Computational Physics. (A preprint is available on the arXiv.) This paper systematically tests the accuracy of the immersed finite element/difference method (IBFEMethod in IBAMR) using different regularized delta functions and relative mesh densities for several benchmark problems along with our large-scale model of a bioprosthetic heart valve in a pulse duplicator. 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 this condition. We also find that narrower kernels are more robust, in the sense that they yield results that are less sensitive to relative changes in the Eulerian and Lagrangian mesh spacings, 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. I think this will be a very useful study for practitioners of the IB method.

Congratulations, Mike!

We are trilled to announce that we just received notification of a new $2.7M NIH R01 award for a project that aims to create and use experimentally and clinically validated computer models to understand the mechanisms that lead to subclinical leaflet thrombosis in bioprosthetic heart valves following aortic valve replacement, and thereby improve risk stratification and device selection for patients who require aortic valve replacement to treat aortic stenosis.

This is a collaborative project that will be carried out with teams of researchers at the University of California, Irvine (PI: Arash Kheradvar) and the University of Utah (PI: Aaron Fogelson) along with collaborators here at UNC School of Medicine.

Aaron Barrett’s paper, A hybrid semi-Lagrangian cut cell method for advection-diffusion problems with Robin boundary conditions in moving domains, has been accepted to appear in Journal of Computational Physics. (A preprint is available on the arXiv.) This paper introduces a new discretization approach to advection-diffusion equations with Robin boundary conditions on complex time-dependent domains. This work is part of broader efforts to simulate thrombosis in atrial fibrillation and leaflet thrombosis following aortic heart valve replacement.

Congratulations, Aaron!

Bryn Barker has been selected to the 2021-2022 incoming class of DOE Computational Graduate Fellowship program. (For more information about this program, see the announcement from the Krell Institute.)

Congratulations, Bryn!!

Jordan Brown has been selected to be the Senior Teaching Fellow in the Department of Mathematics for the 2021-2022 academic year.

Congratulations, Jordan!!

Saad Qadeer’s paper, The smooth forcing extension method: A high-order technique for solving elliptic equations on complex domains, has been accepted to appear in Journal of Computational Physics. (A preprint is available on the arXiv.) This paper introduces a new high-order accurate approach, the smooth forcing extension method, to elliptic equations in complex geometries using Fourier continuation methods.

The smooth forcing extension method is similar to the immersed boundary smooth extension (IBSE) method introduced by Guy, Stein, Thomases, and co-workers, but it relies on extending the forcing term instead of the solution field from the “physical” to the “non-physical” domain. One consequence of this difference is that the smooth forcing extension method can yield a better conditioned system of equations than the IBSE formulation, which can yield improved accuracy at higher resolutions.

Congratulations, Saad!

Amin Kolahdouz’s paper, A sharp interface Lagrangian-Eulerian method for rigid-body fluid-structure interaction, has been accepted to appear in Journal of Computational Physics. (A preprint is available on the arXiv.) This paper introduces a new sharp interface method to simulate fluid-structure interaction (FSI) involving rigid bodies immersed in viscous incompressible fluids by substantially extending Amin’s earlier work on immersed interface methods for discrete surfaces.

We refer to the numerical approach developed in this paper as an immersed Lagrangian-Eulerian (ILE) method. This ILE method integrates aspects of partitioned and immersed FSI formulations: it solves separate momentum equations for the fluid and solid subdomains, as in a partitioned formulation, while also using non-conforming discretizations of the dynamic fluid and structure regions, as in an immersed formulation.

An important aspect of the methodology is that, at least for all of the tests considered so far, it does not appear to suffer from so-called added mass effect instabilities. Indeed, tests suggest that it is capable of treating models with extremely small, nearly equal, equal, and large solid-fluid density ratios. The question of whether the ILE method does or does not suffer from the added mass effect awaits future analytical studies.

We are looking forward to future extensions and applications of this exciting new approach to FSI.

Congratulations, Amin!

Mike Lee’s paper with Robert Hunt and others, Bioprosthetic aortic valve diameter and thickness are directly related to leaflet fluttering: Results from a combined experimental and computational modeling study, has been accepted to appear in JTCVS Open, the open-access mirror of the Journal of Thoracic and Cardiovascular Surgery. This study demonstrates that bioprosthetic heart valves with smaller diameters and/or thicker leaflets generate higher fluttering frequencies in experimental and computational pulse duplicators. Because fluttering can impair the durability of flexible structures, extensions of this work may ultimately lead to new device design targets or selection guidelines to improve the durability of valve replacement.

Congratulations, Mike!

Jianhua Qin’s paper with Amin, An immersed interface-lattice Boltzmann method for fluid-structure interaction, has been accepted to appear in Journal of Computational Physics. (A preprint is available on the arXiv.) This paper develops what is, so far as we know, the first extension of the immersed interface method to lattice Boltzmann method-based descriptions of fluid flows.

Congratulations, Jianhua!