Year: 2025
Type: article
Abstract: In the class of immersed boundary (IB) methods, the choice of the regularized delta function plays a crucial role in transferring information between fluid and solid domains through interpolation and spreading operators. Most prior work using the IB method has used isotropic kernels that do not preserve the divergence-free condition of the velocity field, leading to loss of incompressibility of the solid when interpolating the Eulerian velocity to Lagrangian markers. One approach to addressing this issue in IB simulations involving large deformations of immersed incompressible elastic structures is to use a volumetric stabilization approach, such as adding a volumetric energy term and using modified invariants in the structure's constitutive model. Composite B-spline (CBS) kernels offer an alternative approach by inherently maintaining the discrete divergence-free property. This work evaluates the performance of CBS kernels in terms of their volume conservation and accuracy, comparing them with several traditional isotropic kernel functions using a construction introduced by Peskin (referred to as IB kernels) and B-spline (BS) kernels. Benchmark tests include pressure-loaded and shear-dominated flows, such as an elastic band under differential pressure loads, a pressurized membrane, a compressed block, Cook's membrane, a slanted channel flow, and a modified Turek-Hron problem. Additionally, we validate our methodology using a complex fluid-structure interaction model of bioprosthetic heart valve dynamics in a pulse duplicator. Results demonstrate that CBS kernels achieve superior volume conservation compared to conventional isotropic kernels, eliminating the need for additional volumetric stabilization techniques typically required to address instabilities arising from volume conservation errors. Further, it is common that the accuracy provided by CBS kernels on coarser grids is comparable to that provided by IB and BS kernels on finer grids. Unlike IB and BS kernels, which perform better with larger mesh ratio factors between solid and fluid grids, CBS kernels show improved results with smaller mesh ratio factors. Additionally, the study reveals that although wider kernels provide more accurate results across all methods, CBS kernels are less sensitive to variations in relative grid spacings than isotropic kernels. This study highlights the advantages of CBS kernels in achieving stable, accurate, and efficient FSI simulations without requiring specialized volumetric stabilization treatments when simulating large deformations of elastic solids immersed in fluid.
DOI: 10.3934/acse.2025011
Institution: University of North Carolina at Chapel Hill
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Funders: National Science Foundation, U.S. Department of Defense, National Institutes of Health, University of North Carolina at Chapel Hill, National Defense Science and Engineering Graduate, National Heart, Lung, and Blood Institute, National Institute of Diabetes and Digestive and Kidney Diseases, Division of Chemical, Bioengineering, Environmental, and Transport Systems
Awards: Collaborative Research: Frameworks: Multiphase Fluid-Structure Interaction Software Infrastructure to Enable Applications in Medicine, Biology, and Engineering, CAREER: Numerical Methods and Computational Infrastructure for Simulating Prosthetic Heart Valve Function and Dysfunction, NSF/FDA SIR: Patient-Specific Computational Assessment of Inferior Vena Cava Filter Performance, SI2-SSI: Collaborative Research: Scalable Infrastructure for Enabling Multiscale and Multiphysics Applications in Fluid Dynamics, Solid Mechanics, and Fluid-Structure Interaction, G7792314235, G9000022097, Computational and Experimental Modeling of Subclinical Leaflet Thrombosis in Bioprosthetic Aortic Valves, Modulation of VSMC phenotype through the Insulin Receptor Substrate-1/Kruppel-like factor-4 signal transduction pathway: a Novel Target for AVF Dysfunction
OpenAlex ID: W4409436087