Remarks on a Fluid-Structure Interaction Scheme Based on the Least-Squares Finite Element Method at Small Strains

Nisters, Carina; Schwarz, Alexander; Averweg, Solveigh; Schröder, Jörg

doi:10.1007/978-3-319-70563-7_12

Cited by 3 publications

(3 citation statements)

References 42 publications

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“…with the pressure p, the fluid density ρ f and the kinematic viscosity ν f . For more details, see, e.g., [1], [5] and [6]. To consider the deformation of the fluid domain, an Arbitrary-Lagrangian-Eulerian framework is used by introducing a mesh velocityṽ, which is determined with a linear elasticity approach and subtracted from the fluid velocity.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

A least‐squares finite element approach to model fluid‐structure interaction problems

Averweg

Schwarz

Nisters

et al. 2019

Proc Appl Math and Mech

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In this contribution an approach to model fluid-structure interaction (FSI) problems with monolithic coupling is presented. The fluid as well as the structural domain are discretized using the least-squares finite element method (LSFEM), whose application results in a minimization problem with symmetric positive definite systems also for non self-adjoint operators, see e.g. [2]. In this study, the second-order systems are reduced to first-order systems by introducing new variables, which leads to least-squares formulations for both domains based on the stresses and velocities as presented in e.g.[5] and [7]. A conforming discretization of the unknown fields in H 1 and H(div) using Lagrange interpolation polynomials and vector-valued Raviart-Thomas interpolations functions, respectively, leads to the inherent fulfillment of the FSI coupling conditions. In more detail, a discretization in H 1 ensures continuity of the velocity field and a discretization in H(div) results in continuity of the normal stress components at the interface.

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Section: Theoretical Frameworkmentioning

confidence: 99%

A least‐squares finite element approach to model fluid‐structure interaction problems

Averweg

Schwarz

Nisters

et al. 2019

Proc Appl Math and Mech

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“…, with the weighting factors chosen as ω 1 = ∆t/ρ, ω 2 = 1/(ρν) and ω 3 = 1 based on the findings in [3]. For further information on the construction and minimization of (time discretized) LS functionals and the choice of appropriate weighting terms see [4], for instance.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

“…The required formulas for the implementation of all schemes are summarized in Table 1. For detailed information on the discretization methods, the reader is referred to [3], [5] and [6], for instance.…”

Section: Discretization In Timementioning

confidence: 99%

Implicit time discretization schemes for least‐squares finite element formulations to model incompressible flows

Averweg

Schwarz

Nisters

et al. 2018

Proc Appl Math and Mech

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In the present contribution different implicit time integration schemes to model incompressible flow problems are investigated. Amongst the tested methods are the fully implicit Newmark, Houbolt and Crank-Nicolson schemes.The first-order system for the proposed formulation is given in terms of stresses and velocities as introduced in [1]. Raviart-Thomas and standard Lagrange interpolation functions are used to approximate the stresses and velocities, respectively.For the comparison of all time discretization schemes, the unsteady two-dimensional laminar flow around a cylinder at Reynolds number Re = 100 is chosen. For a rating on the accuracy, the obtained results for the drag coefficient are benchmarked against reference solutions by [2].

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A monolithic fluid–structure interaction approach using mixed LSFEM with high-order time integration

Averweg,

Schwarz,

Schwarz

et al. 2024

Computer Methods in Applied Mechanics and Engineering

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Remarks on a Fluid-Structure Interaction Scheme Based on the Least-Squares Finite Element Method at Small Strains

Cited by 3 publications

References 42 publications

A least‐squares finite element approach to model fluid‐structure interaction problems

A least‐squares finite element approach to model fluid‐structure interaction problems

Implicit time discretization schemes for least‐squares finite element formulations to model incompressible flows

A monolithic fluid–structure interaction approach using mixed LSFEM with high-order time integration

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