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Recent advancements have demonstrated that fully Eulerian methods can effectively model frictionless contact between deformable solids. Unlike traditional Lagrangian approaches, which require contact detection and resolution algorithms, the…

Soft Condensed Matter · Physics 2024-12-20 Flavio Lorez , Mohit Pundir

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 introduce an Eulerian approach for problems involving one or more soft solids immersed in a fluid, which permits mechanical interactions between all phases. The reference map variable is exploited to simulate finite-deformation…

Computational Physics · Physics 2015-12-16 Boris Valkov , Chris H. Rycroft , Ken Kamrin

Elastic contact in hydrodynamic environments is a complex multiphysics phenomenon and can be found in applications ranging from engineering to biological systems. Understanding the intricacies of this coupled problem requires the…

Fluid Dynamics · Physics 2024-09-17 Biswajeet Rath , Xiaoyu Mao , Rajeev K. Jaiman

We present a fully Eulerian hybrid immersed-boundary/phase-field model to simulate wetting and contact line motion over any arbitrary geometry. The solid wall is described with a volume-penalisation ghost-cell immersed boundary whereas the…

Fluid Dynamics · Physics 2021-06-30 Armin Shahmardi , Marco Edoardo Rosti , Outi Tammisola , Luca Brandt

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

In this paper, we present an Eulerian-Lagrangian methodology to simulate the interaction between a fluid-fluid interface and a solid particle in the presence of wetting effects. The target physical problem is represented by ternary phase…

Fluid Dynamics · Physics 2023-09-21 Fernando Kevin Miranda S. Cruz , Cristian Marchioli

In this paper, we develop a novel phase-field model for fluid-structure interaction (FSI), that is capable to handle very large deformations as well as topology changes like contact of the solid to the domain boundary. The model is based on…

Computational Physics · Physics 2023-05-03 Dominic Mokbel , Helmut Abels , Sebastian Aland

In this paper, we present a novel interface-driven adaptive variational procedure using a fully Eulerian description of fluid-structure interaction. The proposed fully-Eulerian procedure involves a fixed background unstructured mesh on…

Computational Physics · Physics 2022-02-08 Biswajeet Rath , Xiaoyu Mao , Rajeev K. Jaiman

We develop a computational method based on an Eulerian field called the "reference map", which relates the current location of a material point to its initial. The reference map can be discretized to permit finite-difference simulation of…

Soft Condensed Matter · Physics 2009-05-07 Ken Kamrin , Jean-Christophe Nave

Frictional sliding contact in hydrodynamic environments can be found in a range of engineering applications. Accurate modeling requires an integrated numerical framework capable of resolving large relative motions, multiphase interactions,…

Computational Physics · Physics 2025-10-01 Biswajeet Rath , Rajeev K. Jaiman

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

In this work, we develop a cut-based unfitted finite element formulation for solving nonlinear, nonstationary fluid-structure interaction with contact in Eulerian coordinates. In the Eulerian description fluid flow modeled by the…

Numerical Analysis · Mathematics 2025-03-24 Stefan Frei , Tobias Knoke , Marc C. Steinbach , Anne-Kathrin Wenske , Thomas Wick

We analyze a phase-field approximation of a sharp-interface model for two- phase materials proposed by M. Silhavy [32, 33]. The distinguishing trait of the model resides in the fact that the interfacial term is Eulerian in nature, for it is…

Mathematical Physics · Physics 2019-05-22 Diego Grandi , Martin Kruzik , Edoardo Mainini , Ulisse Stefanelli

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…

Numerical Analysis · Mathematics 2017-02-27 Boyce E. Griffith , Xiaoyu Luo

We propose a sharp-interface model for a hyperelastic material consisting of two phases. In this model, phase interfaces are treated in the deformed configuration, resulting in a fully Eulerian interfacial energy. In order to penalize large…

Analysis of PDEs · Mathematics 2024-02-16 Katharina Brazda , Martin Kružík , Fabian Rupp , Ulisse Stefanelli

A novel method for complex fluid-structure interaction (FSI) involving large structural deformation and motion is proposed. The new approach is based on a hybrid fluid formulation that combines the advantages of purely Eulerian (fixed-grid)…

Computational Engineering, Finance, and Science · Computer Science 2018-08-02 Benedikt Schott , Christoph Ager , Wolfgang A. Wall

Surface growth, i.e., the addition or removal of mass from the boundary of a solid body, occurs in a wide range of processes, including the growth of biological tissues, solidification and melting, and additive manufacturing. To understand…

Analysis of PDEs · Mathematics 2025-02-25 S. Kiana Naghibzadeh , Anthony Rollett , Noel Walkington , Kaushik Dayal

Numerical simulations are essential for evaluating the performance and safety of geological engineered systems such as geologic carbon storage sites, enhanced geothermal fields, and oil and gas reservoirs. A key challenge lies in accurately…

Numerical Analysis · Mathematics 2025-09-26 Matteo Frigo , Nicola Castelletto , Matteo Cusini , Randolph R. Settgast , Hamdi A. Tchelepi

The fluid structure interaction of cylinders in tandem arrangement is used as validation basis of a multi-domain Lagrangian-Eulerian hybrid flow solver. In this hybrid combination, separate grids of limited width are defined around every…

Fluid Dynamics · Physics 2022-07-20 George Papadakis , Vasilis A. Riziotis , Spyros G. Voutsinas
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