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Stabilised mixed velocity-pressure formulations are one of the widely-used finite element schemes for computing the numerical solutions of laminar incompressible Navier-Stokes. In these formulations, the Newton-Raphson scheme is employed to…

Computational Engineering, Finance, and Science · Computer Science 2020-07-15 Chennakesava Kadapa , Wulf G Dettmer , Djordje Peric

Accurate numerical simulation of coupled fracture/fault deformation and fluid flow is crucial to the performance and safety assessment of many subsurface systems. In this work, we consider the discretization and enforcement of contact…

Numerical Analysis · Mathematics 2020-06-11 Andrea Franceschini , Nicola Castelletto , Joshua A. White , Hamdi A. Tchelepi

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…

In this paper, a simple field function is presented for facilitating the solution of complex and dynamic fluid-solid systems on Cartesian grids with interface-resolved fluid-fluid, fluid-solid, and solid-solid interactions. For a…

Computational Physics · Physics 2018-04-20 Huangrui Mo , Fue-Sang Lien , Fan Zhang , Duane S. Cronin

A new simulation method for solving fluid-structure coupling problems has been developed. All the basic equations are numerically solved on a fixed Cartesian grid using a finite difference scheme. A volume-of-fluid formulation (Hirt and…

Computational Physics · Physics 2015-05-20 Kazuyasu Sugiyama , Satoshi Ii , Shintaro Takeuchi , Shu Takagi , Yoichiro Matsumoto

Plants live in constantly moving fluid, whether air or water. In response to the loads associated with fluid motion, plants bend and twist, often with great amplitude. These large deformations are not found in traditional engineering…

Soft Condensed Matter · Physics 2020-12-07 Frederick P. Gosselin

A new computational method is presented to resolve hydrodynamic interactions acting on solid particles immersed in incompressible host fluids. In this method, boundaries between solid particles and host fluids are replaced with a continuous…

Soft Condensed Matter · Physics 2009-11-10 Y. Nakayama , R. Yamamoto

Soft lubricated contacts exhibit complex interfacial behaviours governed by the coupled effects of multiscale surface roughness and non-linear fluid-solid interactions. Accurately capturing this interplay across thin-film flows is…

Soft Condensed Matter · Physics 2025-11-12 Qian Wang , Suhaib Ardah , Tom Reddyhoff , Daniele Dini

A preconditioning framework for the coupled problem of frictional contact mechanics and fluid flow in the fracture network is presented. The porous medium is discretized using low-order continuous finite elements, with cell-centered…

Numerical Analysis · Mathematics 2022-05-25 Andrea Franceschini , Laura Gazzola , Massimiliano Ferronato

The goal of this paper is to test solids4Foam, the fluid-structure interaction (FSI) toolbox developed for foam-extend (a branch of OpenFOAM), and assess its flexibility in handling more complex flows. For this purpose, we consider the…

Fluid Dynamics · Physics 2021-05-04 Michele Girfoglio , Annalisa Quaini , Gianluigi Rozza

In microscopic mechanical systems interactions between elastic structures are often mediated by the hydrodynamics of a solvent fluid. At microscopic scales the elastic structures are also subject to thermal fluctuations. Stochastic…

Soft Condensed Matter · Physics 2023-02-28 Paul J. Atzberger

In this paper, we study an interaction problem between a $3D$ compressible viscous fluid and a $3D$ nonlinear viscoelastic solid fully immersed in the fluid, coupled together on the interface surface. The solid is allowed to have…

Analysis of PDEs · Mathematics 2023-12-20 Malte Kampschulte , Boris Muha , Srđan Trifunović

We present a novel (high-order) hybridizable discontinuous Galerkin (HDG) scheme for the fluid-structure interaction (FSI) problem. The (moving domain) incompressible Navier-Stokes equations are discretized using a divergence-free HDG…

Numerical Analysis · Mathematics 2021-03-30 Guosheng Fu

Different formulations of interfacial force have been adopted in phase-field-based lattice Boltzmann method for two-phase flows. Although they are identical mathematically, their numerical performances may be different due to truncation…

Fluid Dynamics · Physics 2021-06-16 Chunhua Zhang , Hong Liang , Zhaoli Guo

We propose a novel solid-fluid interaction method for coupling elastic solids with impulse flow maps. Our key idea is to unify the representation of fluid and solid components as particle flow maps with different lengths and dynamics. The…

Graphics · Computer Science 2024-09-17 Duowen Chen , Zhiqi Li , Junwei Zhou , Fan Feng , Tao Du , Bo Zhu

When simulating three-dimensional flows interacting with deformable and elastic obstacles, current methods often encounter complexities in the governing equations and challenges in numerical implementation. In this work, we introduce a…

Fluid Dynamics · Physics 2026-01-09 Andreu F. Gallen , Joan Muñoz Biosca , Mario Castro , Aurora Hernández-Machado

In this paper we advance the analysis of discretizations for a fluid-structure interaction model of the monolithic coupling between the free flow of a viscous Newtonian fluid and a deformable porous medium separated by an interface. A…

Numerical Analysis · Mathematics 2023-06-27 Wietse M. Boon , Martin Hornkjøl , Miroslav Kuchta , Kent-Andre Mardal , Ricardo Ruiz-Baier

Deep learning has shown promise in improving computing efficiency while ensuring modeling accuracy in fluid-structure interaction (FSI) analysis. However, its current capabilities are limited when it comes to constructing multi-object…

Fluid Dynamics · Physics 2025-04-25 Yanfang Lyu , Yunyang Zhang , Zhiqiang Gong , Xiao Kang , Wen Yao , Yongmao Pei

We consider the method of mappings for performing shape optimization for unsteady fluid-structure interaction (FSI) problems. In this work, we focus on the numerical implementation. We model the optimization problem such that it takes…

Optimization and Control · Mathematics 2024-06-21 Johannes Haubner , Michael Ulbrich

We present a distributed Lagrange multiplier formulation of the Finite Element Immersed Boundary Method to couple incompressible fluids with compressible solids. This is a generalization of the formulation presented in Heltai and Costanzo…

Numerical Analysis · Mathematics 2017-12-08 Daniele Boffi , Lucia Gastaldi , Luca Heltai