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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

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

Computational fluid dynamics (CFD) has become a cornerstone of modern water engineering, providing quantitative tools for the analysis, prediction, and management of complex hydraulic systems across a wide range of spatial and temporal…

Fluid Dynamics · Physics 2025-12-19 Anshu Kumar , Kemi Olimba , Vyacheslav Kungurtsev , Fabio V. Difonzo

In this work we develop a fictitious domain method for the Stokes problem which allows computations in domains whose boundaries do not depend on the mesh. The method is based on the ideas of Xfem and has been first introduced for the…

Numerical Analysis · Mathematics 2014-01-06 Sébastien Court , Michel Fournié , Alexei Lozinski

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 consider the motion of a rigid body immersed in a two-dimensional viscous incompressible fluid with Navierslip-with-friction conditions at the solid boundary. The fluid-solid system occupies the whole plane. We provethe small-time exact…

Analysis of PDEs · Mathematics 2018-07-19 József Kolumbán

We extend the recently introduced divergence-conforming immersed boundary (DCIB) method [1] to fluid-structure interaction (FSI) problems involving closed co-dimension one solids. We focus on capsules and vesicles, whose discretization is…

We present a novel computational modeling framework to numerically investigate fluid-structure interaction in viscous fluids using the phase field embedding method. Each rigid body or elastic structure immersed in the incompressible viscous…

Fluid Dynamics · Physics 2021-09-16 Qi Hong , Qi Wang

We present a novel framework inspired by the Immersed Boundary Method for predicting the fluid-structure interaction of complex structures immersed in flows with moderate to high Reynolds numbers. The main novelties of the proposed…

Modern techniques for physical simulations rely on numerical schemes and mesh-refinement methods to address trade-offs between precision and complexity, but these handcrafted solutions are tedious and require high computational power.…

Machine Learning · Computer Science 2024-02-21 Janny Steeven , Nadri Madiha , Digne Julie , Wolf Christian

Matching the swimming efficiency and agility of fish has remained an elusive goal in underwater robotics. Such locomotion capabilities rely on complex vortex interactions between the robot's body and the surrounding fluid. However,…

Robotics · Computer Science 2026-05-28 Jeong Hun Lee , Junzhe Hu , Sofia Kwok , Carmel Majidi , Zachary Manchester

Simulating the interaction of fluids with immersed moving solids is playing an important role for gaining a better quantitative understanding of how fluid dynamics is altered by the presence of obstacles and which forces are exerted on the…

We consider a rigid body freely moving in a compressible inviscid fluid within a bounded domain $\Omega\subset\mathbb{R}^3$. The fluid is thereby governed by the non necessarily isentropic compressible Euler equations, while the rigid body…

Analysis of PDEs · Mathematics 2025-12-11 Frédéric Rousset , Pei Su

Two methods for solid body representation in flow simulations available in the Pencil Code are the immersed boundary method and overset grids. These methods are quite different in terms of computational cost, flexibility and numerical…

Computational Physics · Physics 2018-11-20 Jørgen R. Aarnes , Tai Jin , Chaoli Mao , Nils E. L. Haugen , Kun Luo , Helge I. Andersson

In this work, the Immersed Boundary Method (IBM) with feedback forcing introduced by Goldstein et al. (1993) and often referred in the literature as the Virtual Boundary Method (VBM), is addressed. The VBM has been extensively applied both…

Numerical Analysis · Mathematics 2021-10-25 Michele Girfoglio , Giovanni Stabile , Andrea Mola , Gianluigi Rozza

The immersed boundary (IB) method has been used as a means to simulate fluid-membrane interactions in a wide variety of biological and engineering applications. Although the numerical convergence of the method has been empirically verified,…

Numerical Analysis · Mathematics 2025-10-09 Alexandre X. Milewski , Charles S. Peskin

In this paper, the Immersed Boundary Method (IBM) proposed by Pinelli is implemented for finite volume approximations of incompressible Navier-Stokes equations solutions in the open source toolbox OpenFOAM version 2.2. Solid obstacles are…

Fluid Dynamics · Physics 2016-09-15 E. Constant , C. Li , J. Favier , M. Meldi , P. Meliga , E. Serre

We study the motion of a rigid body within a compressible, isentropic, and viscous fluid contained in a fixed bounded domain $\Omega \subset \mathbb{R}^3$. The fluid's behavior is described by the Navier-Stokes equations, while the motion…

Analysis of PDEs · Mathematics 2024-08-15 Šimon Axmann , Šárka Nečasová , Ana Radošević

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

We present a fluctuating boundary integral method (FBIM) for overdamped Brownian Dynamics (BD) of two-dimensional periodic suspensions of rigid particles of complex shape immersed in a Stokes fluid. We develop a novel approach for…

Numerical Analysis · Mathematics 2018-09-26 Yuanxun Bao , Manas Rachh , Eric Keaveny , Leslie Greengard , Aleksandar Donev