ArticleInternational journal for numerical methods in biomedical engineering2017
Hybrid finite difference/finite element immersed boundary method.
Article in International journal for numerical methods in biomedical engineering, 2017. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 43 papers.
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43 citing papers in PubMed.
- Article
- Composite B-spline regularized delta functions for the immersed boundary method: Divergence-free interpolation and gradient-preserving force spreading.Journal of computational physics · 2026Article
- Improving the robustness of the immersed interface method through regularized velocity reconstruction.Journal of computational physics · 2026Article
- An open-source computational framework for immersed fluid-structure interaction modeling using FEBio and MFEM.Engineering with computers · 2026Article
- Article
- A numerical framework for preprocedural prosthetic valve positioning and hemodynamic evaluation.Biomechanics and modeling in mechanobiology · 2025Article
- LOCAL DIVERGENCE-FREE IMMERSED FINITE ELEMENT-DIFFERENCE METHOD USING COMPOSITE B-SPLINES.Advances in computational science and engineering · 2025Article
- Three-dimensional fluid-structure interaction modelling of the venous valve using immersed boundary/finite element method.Computers in biology and medicine · 2025Article
- Simulating cardiac fluid dynamics in the human heart.PNAS nexus · 2024Article
- Benchmarking the Immersed Boundary Method for Viscoelastic Flows.Journal of computational physics · 2024Article
- Current progress toward isogeometric modeling of the heart biophysics.Biophysics reviews · 2023Review
- An immersed peridynamics model of fluid-structure interaction accounting for material damage and failure.Journal of computational physics · 2023Article
- A sharp interface Lagrangian-Eulerian method for flexible-body fluid-structure interaction.Journal of computational physics · 2023Article
- A model of fluid-structure and biochemical interactions for applications to subclinical leaflet thrombosis.International journal for numerical methods in biomedical engineering · 2023Article
- A Nodal Immersed Finite Element-Finite Difference Method.Journal of computational physics · 2023Article
- Semi-Automated Construction of Patient-Specific Aortic Valves from Computed Tomography Images.Annals of biomedical engineering · 2023Article
- On the Lagrangian-Eulerian Coupling in the Immersed Finite Element/Difference Method.Journal of computational physics · 2022Article
- A fully resolved multiphysics model of gastric peristalsis and bolus emptying in the upper gastrointestinal tract.Computers in biology and medicine · 2022Article
- Structural engineering from an inverse problems perspective.Proceedings. Mathematical, physical, and engineering sciences · 2022Review
- Exploring the sensitivity in jellyfish locomotion under variations in scale, frequency, and duty cycle.Journal of mathematical biology · 2021Article
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Abstract
The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and even now, most immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian variables that facilitates independent spatial discretizations for the structure and background grid. This approach uses a finite element discretization of the structure while retaining a finite difference scheme for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes. The Lagrangian-Eulerian coupling approach developed in this work enables the effective use of these coarse structural meshes with the immersed boundary method. This work also contrasts two different weak forms of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations facilitated by our coupling approach.
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