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The immersed boundary method is a numerical and mathematical formulation for solving fluid-structure interaction problems. It relies on solving fluid equations on an Eulerian fluid grid and interpolating the resulting velocity back onto…

Numerical Analysis · Mathematics 2020-03-19 Ondrej Maxian , Charles S. Peskin

We describe a general phase-field model for hyperelastic multiphase materials. The model features an elastic energy functional that depends on the phase-field variable and a surface energy term that depends in turn on the elastic…

Analysis of PDEs · Mathematics 2020-05-13 Diego Grandi , Martin Kružík , Edoardo Mainini , Ulisse Stefanelli

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 present a hybrid partitioned deep learning framework for the reduced-order modeling of fluid-structure interaction. Using the discretized Navier-Stokes in the arbitrary Lagrangian-Eulerian reference frame, we generate the full-order flow…

Fluid Dynamics · Physics 2021-11-02 Rachit Gupta , Rajeev Kumar Jaiman

We present a strongly-coupled immersed-boundary method for flow-structure interaction problems involving thin deforming bodies. The method is stable for arbitrary choices of solid-to-fluid mass ratios and for large body motions. As with…

Fluid Dynamics · Physics 2016-10-05 Andres Goza , Tim Colonius

This paper deals with the numerical modelling of the interaction between a fluid and an incompressible solid (Neo Hookean) in small perturbations with the lattice Boltzmann method (LBM). In order to use a monolithic formulation and to solve…

Computational Physics · Physics 2020-11-18 Sébastien Mey , Erwan Liberge , Claudine Béghein

We studied numerically the dynamics of colliding rigid bodies in a Newtonian fluid. The finite element method is used to solve the fluid-body interaction and the fluid motion is described in the Arbitrary-Lagrangian-Eulerian framework. To…

This work describes three diffuse-interface methods for the simulation of immiscible, compressible multiphase fluid flows and elastic-plastic deformation in solids. The first method is the localized-artificial-diffusivity approach of Cook…

Computational Physics · Physics 2021-09-21 Suhas S. Jain , Michael C. Adler , Jacob R. West , Ali Mani , Parviz Moin , Sanjiva K. Lele

The immersed boundary method is a mathematical framework for modeling fluid-structure interaction. This formulation describes the momentum, viscosity, and incompressibility of the fluid-structure system in Eulerian form, and it uses…

Numerical Analysis · Mathematics 2020-02-26 Ben Vadala-Roth , Shashank Acharya , Neelesh A Patankar , Simone Rossi , Boyce E Griffith

We present a hybrid Eulerian-Lagrangian method for the direct simulation of three-dimensional, heterogeneous structures made of soft fibers and immersed in incompressible viscous fluids. Fiber-based organization of matter is pervasive in…

Computational Physics · Physics 2024-01-19 Arman Tekinalp , Yashraj Bhosale , Songyuan Cui , Fan Kiat Chan , Mattia Gazzola

In this paper, we present a novel approach to model the fluid/solid interaction forces in a direct solver of the Navier-Stokes equations based on the volume of fluid interface tracking method. The key ingredient of the model is the explicit…

Fluid Dynamics · Physics 2015-06-16 Kyle Mahady , Shahriar Afkhami , Lou Kondic

We evaluate a number of different finite element approaches for fluid-structure (contact) interaction problems against data from physical experiments. For this we take the data from experiments by Hagemeier [Mendeley Data, doi:…

Fluid Dynamics · Physics 2021-03-03 Henry von Wahl , Thomas Richter , Stefan Frei , Thomas Hagemeier

The problem of multiphase materials (fluid or solid) interacting with the rigid body structure is studied by proposing a novel VMS-FEM (variational multi-scale finite element method) in the Eulerian framework using the fixed mesh. The…

Numerical Analysis · Mathematics 2023-03-21 Tianyu Li

We devise an iterative scheme for numerically calculating dynamical two-point correlation functions in integrable many-body systems, in the Eulerian scaling limit. Expressions for these were originally derived in Ref. [1] by combining the…

Statistical Mechanics · Physics 2021-01-01 Frederik S. Møller , Gabriele Perfetto , Benjamin Doyon , Jörg Schmiedmayer

Direct numerical simulations of turbulent flow in a channel with one rigid and one viscoelastic wall are performed. An Eulerian-Eulerian model is adopted with a level-set approach to identify the fluid-compliant material interface. Focus is…

Fluid Dynamics · Physics 2021-11-03 Amir Esteghamatian , Joseph Katz , Tamer A. Zaki

We present an adaptive reduced-order model for the efficient time-resolved simulation of fluid-structure interaction problems with complex and non-linear deformations. The model is based on repeated linearizations of the structural balance…

Fluid Dynamics · Physics 2020-04-13 Ali Thari , Vito Pasquariello , Niels Aage , Stefan Hickel

This paper proposes a new general methodology for finite-time singularity formation for moving interface problems involving the incompressible Euler equations in the plane. The first problem considered is the two-phase Euler vortex sheets…

Analysis of PDEs · Mathematics 2017-09-04 Daniel Coutand

We present a method for computing fluid-structure interaction problems for multi-body systems. The fluid flow equations are solved using a fractional-step method with the immersed boundary method proposed by Uhlmann [J. Comput Phys. 209…

We present an accurate Lagrangian method based on vortex particles, level-sets, and immersed boundary methods, for animating the interplay between two fluids and rigid solids. We show that a vortex method is a good choice for simulating…

Numerical Analysis · Mathematics 2016-08-16 Mathieu Coquerelle , Jérémie Allard , Georges-Henri Cottet , Marie-Paule Cani

Many multiphase fluid systems, such as those involving immiscible polymers or liquid-liquid systems with surfactants, have shown a breakdown of the no-slip condition at the material interface. This results in systems where the tangential…

Fluid Dynamics · Physics 2023-04-05 Afsoun Rahnama Falavarjani , David Salac