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The aim of this paper is to provide a survey of the state of the art in the finite element approach to the Immersed Boundary Method (FE-IBM) which has been investigated by the authors during the last decade. In a unified setting, we present…

Numerical Analysis · Mathematics 2014-07-22 Daniele Boffi , Lucia Gastaldi

We study the dynamics of elastic interfaces-membranes-immersed in thermally excited fluids. The work contains three components: the development of a numerical method, a purely theoretical approach, and numerical simulation. In developing a…

Soft Condensed Matter · Physics 2009-10-31 Davide Stelitano , Daniel H. Rothman

We consider a nonlinear, moving boundary, fluid-structure interaction problem between a time dependent incompressible, viscous fluid flow, and an elastic structure composed of a cylindrical shell supported by a mesh of elastic rods. The…

Analysis of PDEs · Mathematics 2020-02-17 Sunčica Čanić , Marija Galić , Boris Muha

We present an implementation of a fully variational formulation of an immersed method for fluid-structure interaction problems based on the finite element method. While typical implementation of immersed methods are characterized by the use…

Numerical Analysis · Mathematics 2015-04-10 Saswati Roy , Luca Heltai , Francesco Costanzo

This work focuses on the development and analysis of a partitioned numerical method for moving domain, fluid-structure interaction problems. We model the fluid using incompressible Navier-Stokes equations, and the structure using linear…

Numerical Analysis · Mathematics 2020-07-03 Anyastassia Seboldt , Martina Bukač

The secret to the spectacular flight capabilities of flapping insects lies in their wings, which are often approximated as flat, rigid plates. Real wings are however delicate structures, composed of veins and membranes, and can undergo…

Fluid Dynamics · Physics 2020-02-21 Hung Truong , Thomas Engels , Dmitry Kolomenskiy , Kai Schneider

We present the development and benchmarking of an in-house fluid-structure interaction (FSI) solver. An implicit partitioned approach is utilized to couple a sharp-interface immersed boundary (IB) method based flow solver and a…

Fluid Dynamics · Physics 2020-05-07 Anup Kundu , Atul K. Soti , Hemanshul Garg , Rajneesh Bhardwaj , Mark C. Thompson

This paper presents an immersed boundary (IB) method for fluid--structure--acoustics interactions involving large deformations and complex geometries. In this method, the fluid dynamics is solved by a finite difference method where the…

Fluid Dynamics · Physics 2020-05-20 Li Wang , Fang-Bao Tian , Joseph C. S. Lai

In order to solve the fluid-structure interaction problem of Newtonian fluid, a fluid-structure interaction approach is proposed based on Non-ordinary State-based Peridynamics (NOSB-PD) and Updated Lagrangian particle Hydrodynamics (ULPH),…

Fluid Dynamics · Physics 2024-07-29 Zhen Wang , Junsong Xiong , Xiang Liu , Lisheng Liu , Xin Lai

The immersed boundary (IB) method is a mathematical and numerical framework for problems of fluid-structure interaction, treating the particular case in which an elastic structure is immersed in a viscous incompressible fluid. The IB…

Computational Engineering, Finance, and Science · Computer Science 2017-03-29 Boyce E. Griffith

In this work, we consider fluid-structure interaction simulation with nonlinear hyperelastic models in the solid part. We use a partitioned approach to deal with the coupled nonlinear fluid-structure interaction problems. We focus on…

Numerical Analysis · Mathematics 2013-12-20 Ulrich Langer , Huidong Yang

It is well known that the number of particles should be scaled up to enable industrial scale simulation. The calculations are more computationally intensive when the motion of the surrounding fluid is considered. Besides the advances in…

Computational Physics · Physics 2014-07-28 Hao Zhang , F. Xavier Trias , Assensi Oliva , Dongmin Yang , Yuanqiang Tan , Shi Shu , Yong Sheng

Physics-informed neural networks (PINNs) have emerged as a promising approach for solving complex fluid dynamics problems, yet their application to fluid-structure interaction (FSI) problems with moving boundaries remains largely…

Machine Learning · Computer Science 2025-12-04 Afrah Farea , Saiful Khan , Reza Daryani , Emre Cenk Ersan , Mustafa Serdar Celebi

We present a new composite mesh finite element method for fluid--structure interaction problems. The method is based on surrounding the structure by a boundary-fitted fluid mesh which is embedded into a fixed background fluid mesh. The…

Numerical Analysis · Mathematics 2016-01-20 Andre Massing , Mats G. Larson , Anders Logg , Marie E. Rognes

Using a fixed Eulerian mesh, the phase-field method has been successfully utilized for a broad range of moving boundary problems involving multiphase fluids and single-phase fluid-structure interaction. Nevertheless, multiphase fluids…

Fluid Dynamics · Physics 2024-02-19 Xiaoyu Mao , Rajeev Jaiman

We consider a system of multiple insulating rigid bodies moving inside of an electrically conducting compressible fluid. In this system we take into account the interaction of the fluid with the bodies as well as with the electromagnetic…

Analysis of PDEs · Mathematics 2022-08-15 Jan Scherz

This paper addresses the floating body problem which consists in studying the interaction of surface water waves with a floating body. We propose a new formulation of the water waves problem that can easily be generalized in order to take…

Analysis of PDEs · Mathematics 2016-09-21 David Lannes

Immersed methods discretize boundary conditions for complex geometries on background Cartesian grids. This makes such methods especially suitable for two-way coupled flow-body problems, where the body mechanics are partially driven by…

Fluid Dynamics · Physics 2025-04-01 Xinjie Ji , James Gabbard , Wim M. van Rees

We report development and application of a fluid-structure interaction (FSI) solver for compressible flows with large-scale flow-induced deformation of the structure. The FSI solver utilizes partitioned approach to strongly couple a…

Fluid Dynamics · Physics 2017-05-24 Shantanu Bailoor , Aditya Annangi , Jung Hee Seo , Rajneesh Bhardwaj

We present an enhanced immersed interface method for simulating incompressible fluid flows in thin gaps between closely spaced immersed boundaries. This regime, common in engineered structures such as including tribological interfaces and…

Fluid Dynamics · Physics 2026-03-17 Michael J. Facci , Qi Sun , Boyce E. Griffith
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