A brief summary of finite element method applications to nonlinear wave-structure interactions

Wang, Chizhong; Wu, G.X.

doi:10.1007/s11804-011-1052-7

Cited by 11 publications

(13 citation statements)

References 48 publications

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“…Studies of FNPF solvers based on second-order FEM are plentiful, see, e.g. [26,29,41,42,58,64,70]. FNPF solvers can be derived from Luke's variational principle [39], leading to robust formulations [26,57].…”

Section: On Numerical Fnpf Modelsmentioning

confidence: 99%

A Mixed Eulerian–Lagrangian Spectral Element Method for Nonlinear Wave Interaction with Fixed Structures

2019

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We present a high-order nodal spectral element method for the two-dimensional simulation of nonlinear water waves. The model is based on the mixed Eulerian-Lagrangian (MEL) method. Wave interaction with fixed truncated structures is handled using unstructured meshes consisting of high-order iso-parametric quadrilateral/triangular elements to represent the body surfaces as well as the free surface elevation. A numerical eigenvalue analysis highlights that using a thin top layer of quadrilateral elements circumvents the general instability problem associated with the use of asymmetric mesh topology. We demonstrate how to obtain a robust MEL scheme for highly nonlinear waves using an efficient combination of (i) global L 2 projection without quadrature errors, (ii) mild modal filtering and (iii) a combination of local and global re-meshing techniques. Numerical experiments for strongly nonlinear waves are presented. The experiments demonstrate that the spectral element model provides excellent accuracy in prediction of nonlinear and dispersive wave propagation. The model is also shown to accurately capture the interaction between solitary waves and fixed submerged and surface-piercing bodies. The wave motion and the wave-induced loads compare well to experimental and computational results from the literature. Keywords Nonlinear and dispersive free surface waves • Wave-structure interaction • Fully nonlinear potential flow • Spectral element method • Mixed Eulerian-Lagrangian • Marine hydrodynamics • Numerical wave tank B Carlos Monteserin

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Section: On Numerical Fnpf Modelsmentioning

confidence: 99%

A Mixed Eulerian–Lagrangian Spectral Element Method for Nonlinear Wave Interaction with Fixed Structures

2019

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“…In the studies on fluid behavior, four well-known mesh-based methods can be found in the literature: finite differences method (FDM), finite volume method (FVM), finite element method (FEM) and boundary element method (BEM). The finite element method and the boundary element, and the combination of these two methods in solving problems of fluidstructures interaction have so far been attracting attention of many researchers (Firouz-Abadi et al 2009;Wang and Wu 2011;Nguyen-Thoi et al 2013;Kolaei et al 2015).…”

Section: Introductionmentioning

confidence: 99%

Simulating Fluid and Structure Interaction using Exponential Basis Functions

Abarghooei

Boroomand

2018

JAFM

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In this paper a meshless method using exponential basis functions is developed for fluid-structure interaction in liquid tanks undergoing non-linear sloshing. The formulation in the fluid part is based on the use of Navier-Stokes equations, presented in Lagrangian description as Laplacian of the pressure, for inviscid incompressible fluids. The use of exponential basis functions satisfying the Laplace equation leads to a strong form of volume preservation which has a direct effect on the accuracy of the pressure field. In a boundary node style, the bases are used to incrementally solve the fluid part in space and time. The elastic structure is discretized by the finite elements and analyzed by the Newmark method. The direct use of the pressure, as the 䐀䐀ential of the acceleration, helps to find the loads acting on the structure in a straight-forward manner. The interaction equations are derived and used in the analysis of a tank with elastic walls. The overall formulation may be implemented simply. To demonstrate the efficiency of the solution, the obtained results are compared with those obtained from a finite elements solution using Lagrangian description. The results show that while the wave height and the oscillations of elastic walls of the two analyses are in good agreement with each other; the use of the proposed meshless analysis not only leads to accurate hydrodynamic pressure but also reduces the computational time to one-eighth of the time needed for the finite elements analysis. ☮Keywords: Fluid-structure interaction; Meshless method; Exponential basis functions; Lagrangian

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“…The finite element discretization gives rise to a sparse system of equations, meaning it is much easier to solve in linear time. However, all previous attempts to use a finite element discretization require additional numerical stabilization or specially constructed meshes to prevent numerical instabilities [17][18][19]21,24,25,[27][28][29][30]32].…”

Section: Introductionmentioning

confidence: 99%

“…and(30) are iterated until convergence is reached. In the Jacobian in(29) we use that ∂ a i and ∂ b s, j commute. Recall that S = Φ 11 − Φ 12 Φ −1 22 Φ 21 .…”

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confidence: 99%

Hamiltonian Finite Element Discretization for Nonlinear Free Surface Water Waves

2017

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A novel finite element discretization for nonlinear potential flow water waves is presented. Starting from Luke's Lagrangian formulation we prove that an appropriate finite element discretization preserves the Hamiltonian structure of the potential flow water wave equations, even on general time-dependent, deforming and unstructured meshes. For the time-integration we use a modified Störmer-Verlet method, since the Hamiltonian system is non-autonomous due to boundary surfaces with a prescribed motion, such as a wave maker. This results in a stable and accurate numerical discretization, even for large amplitude nonlinear water waves. The numerical algorithm is tested on various wave problems, including a comparison with experiments containing wave interactions resulting in a large amplitude splash. Keywords Finite element method • Hamiltonian systems • Nonlinear potential flow water wave equations • Symplectic time integration • Moving meshes Mathematics Subject Classification 65M60 • 65P10 • 76B15 B Freekjan Brink

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A brief summary of finite element method applications to nonlinear wave-structure interactions

Cited by 11 publications

References 48 publications

A Mixed Eulerian–Lagrangian Spectral Element Method for Nonlinear Wave Interaction with Fixed Structures

A Mixed Eulerian–Lagrangian Spectral Element Method for Nonlinear Wave Interaction with Fixed Structures

Simulating Fluid and Structure Interaction using Exponential Basis Functions

Hamiltonian Finite Element Discretization for Nonlinear Free Surface Water Waves

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