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The conservation laws of continuum mechanic written in an Eulerian frame make no difference between fluids and solids except in the expression of the stress tensors, usually with Newton's hypothesis for the fluids and Helmholtz potentials…
In this paper, we study a dynamic fluid-structure interaction (FSI) model for an elastic structure that is immersed and spinning in the fluid. We develop a linear constitutive model to describe the motion of a rotational elastic structure…
We present a monolithic finite element formulation for (nonlinear) fluid-structure interaction in Eulerian coordinates. For the discretization we employ an unfitted finite element method based on inf-sup stable finite elements. So-called…
The paper introduces a fully discrete quasi-Lagrangian finite element method for a monolithic formulation of a fluid-porous structure interaction problem. The method is second order in time and allows a standard $P_2-P_1$ (Taylor--Hood)…
Fluid-solid interaction (FSI) problems are fundamental in many scientific and engineering applications, yet effectively capturing the highly nonlinear two-way interactions remains a significant challenge. Most existing deep learning methods…
We develop a three-dimensional Eulerian framework to simulate fluid-structure interaction (FSI) problems on a fixed Cartesian grid using the geometric volume-of-fluid (VOF) method. The coupled problem involves incompressible flow and…
Three-field Fluid-Structure Interaction (FSI) formulations for fluid and solid are applied and compared to the standard two field-one field formulation for fluid and solid, respectively. Both formulations are applied in a non linear setting…
We present a novel partitioned iterative formulation for modeling of fluid-structure interaction in two-phase flows. The variational formulation consists of a stable and robust integration of three blocks of differential equations, viz.,…
We analyse three time integration schemes for unfitted methods in fluid structure interaction. In Alghorithm 1 we propose a fully discrete monolithic algorithm with P1 P1 stabilized finite elements for the fluid problem; for this alghorithm…
Body-fitted arbitrary Lagrangian-Eulerian (ALE) methods provide a sharp representation of the fluid-structure interface but rely on mesh-update strategies that incrementally deform a reference configuration. To address this issue, we…
This work presents a strongly coupled partitioned method for fluid-structure interaction (FSI) problems based on a monolithic formulation of the system which employs a Lagrange multiplier. We prove that both the semi-discrete and fully…
In this work we present a novel monolithic Finite Element Method (FEM) for the hydroelastic analysis of Very Large Floating Structures (VLFS) with arbitrary shapes that is stable, energy conserving and overcomes the need of an iterative…
This work presents a stabilized finite element formulation of the arbitrary Lagrangian-Eulerian (ALE) surface theory for Navier-Stokes flow on self-evolving manifolds developed in Sauer (2025). The formulation is physically frame-invariant,…
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…
In this work, we develop a new algorithm to solve large-scale incompressible time-dependent fluid--structure interaction (FSI) problems using a matrix-free finite element method in arbitrary Lagrangian--Eulerian (ALE) frame of reference. We…
This paper introduces a sharp-interface approach to simulating fluid-structure interaction involving flexible bodies described by general nonlinear material models and across a broad range of mass density ratios. This new flexible-body…
We present a monolithic approach to large-deformation fluid-structure interaction (FSI) problems that allows for choosing fully implicit, single-step and single-stage time integration schemes in the structure and fluid field independently,…
We present a novel second-order semi-implicit hybrid finite volume / finite element (FV/FE) scheme for the numerical solution of the incompressible and weakly compressible Navier-Stokes equations on moving unstructured meshes using an…
This paper introduces a sharp interface method to simulate fluid-structure interaction (FSI) involving rigid bodies immersed in viscous incompressible fluids. The capabilities of this methodology are demonstrated for a range of benchmark…
Based upon two overlapped, body-unfitted meshes, a type of unified-field monolithic fictitious domain-finite element method (UFMFD-FEM) is developed in this paper for moving interface problems of dynamic fluid-structure interactions (FSI)…