Numerical modeling of wave breaking induced by fixed or moving boundaries

Grilli, Stéphan T.; Subramanya, R.

doi:10.1007/bf00363981

Cited by 94 publications

(149 citation statements)

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“…As noted before for wavemakers started from a state of rest (Grilli and Subramanya 1996), at t = 0 there is a discrepancy between the initial (finite) velocity of the heaving …”

Section: Computational Domain and Simulation Methodologymentioning

confidence: 99%

“…In the following, we use notations and definitions introduced in earlier publications of the 2D-FNPF model (Grilli et al 1989;Grilli and Subramanya 1996;Guerber et al 2012; see also the definition section). Thus, the boundary of the fluid domain ∂ f (t) is divided into four parts, on which different types of boundary conditions can be applied,…”

Section: Governing Equationsmentioning

confidence: 99%

“…Following Grilli and Subramanya (1996), in the 2D-HO-BEM model, both the potential and its normal derivative (as well as their time derivative) are discretized by higher-order elements, here, both cubic. This allows computing gradients, such as in the previous equations, by taking the derivative of the shape functions within each boundary element.…”

Section: Mathematical Model and Assumptionsmentioning

confidence: 99%

“…Other numerical methods were also applied, such as the finite element method (FEM) with an arbitrary Lagrangian Eulerian (ALE) formalism to follow the internal points in a 2D numerical wave tank (Yan and Ma 2007); the latter approach was extended to 3D geometry (Ma and Yan 2009). These authors used a direct approach for evaluating the boundary conditions; by contrast, here, we will use an implicit model, based on the earlier work by Guerber et al (2012), who implemented van Daalen's (1993) and Tanizawa's (2000) implicit method in Grilli et al's 2D-FNPF model (Grilli et al 1989;Grilli and Subramanya 1996) to study the interactions of a fluid with fully submerged structures.…”

Section: Introductionmentioning

confidence: 99%

“…In the realm of academic research, since the late 1980s, more advanced and complete models such as FNPF have been developed and used, typically based on a higher-order boundary element method (HO-BEM) (e.g., Grilli et al 1989;Grilli and Subramanya 1996). However, despite a constant increase in computational resources, the coupling of such FNPF models with floating rigid body motion has been mostly studied for two-dimensional (2D) geometry; recent contributions in this respect are based on a BEM solver and a force decomposition method Kim 2004, 2007;Tang et al 2011).…”

Section: Introductionmentioning

confidence: 99%

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Simulation of floating structure dynamics in waves by implicit coupling of a fully non-linear potential flow model and a rigid body motion approach

Dombre

Benoît

Violeau

et al. 2014

J. Ocean Eng. Mar. Energy

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We demonstrate the accuracy and convergence of a new numerical model solving wave-structure interactions based on the fully non-linear potential flow (FNPF) theory coupled to a rigid body motion approach. This work extends an earlier model proposed by Guerber et al. (Eng Anal Bound Elements 36(7):1151-1163, 2012), restricted to fully submerged structures, by allowing to solve for freely floating bodies on the free surface. Although we are currently extending the model to three dimensions (3D), the work reported here only considers two-dimensional (2D) problems. We first introduce the FNPF model, We then detail the numerical scheme used for coupling the FNPF model to the motion of a floating rigid body. Moreover, we propose a new numerical strategy for advancing the free surface front inspired by symplectic integrators, which achieves a much better performance for energy conservation. The developed algorithm is first applied to forced motion cases, for which analytical and experimental results can be found in the literature and used as benchmarks. The accuracy of the numerical solution for the fluid and applied forces is then discussed for cases with small or large amplitude motion. In the latter case, a preliminary investigation of non-linear effects is performed for the classical application of a semi-circular heaving cylinder, by comparing the computed hydrodynamic force to the experimental measurements of Yamashita (J Soc Nav Arch 141: [61][62][63][64][65][66][67][68][69][70] 1977). In particular, the comparison of the magnitude of the force harmonics, up to the third order, shows the importance of simulating non-linear interactions, which become important as the ratio of the radius of the cylinder over the wavelength increases. In a second set of applications, we assess the model accuracy in dealing with freely floating bodies. As a first test case, we consider the decaying motion of a freely heaving horizontal circular cylinder released from a non-equilibrium position above the free surface. In this more demanding computations, we verify that total energy fluid-plus-body motion is well conserved, which confirms the accuracy of the fluid-structure interaction algorithm. As a second test case, we consider the free motion of a rectangular barge in waves and compute the first-order response amplitude operators.

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“…As noted before for wavemakers started from a state of rest (Grilli and Subramanya 1996), at t = 0 there is a discrepancy between the initial (finite) velocity of the heaving …”

Section: Computational Domain and Simulation Methodologymentioning

confidence: 99%

Section: Governing Equationsmentioning

confidence: 99%

Section: Mathematical Model and Assumptionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Simulation of floating structure dynamics in waves by implicit coupling of a fully non-linear potential flow model and a rigid body motion approach

Dombre

Benoît

Violeau

et al. 2014

J. Ocean Eng. Mar. Energy

Self Cite

View full text Add to dashboard Cite

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Lagrangian finite element analysis of Newtonian fluid flows

Radovitzky

Ortiz

1998

Int. J. Numer. Meth. Engng.

104

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A fully Lagrangian finite element method for the analysis of Newtonian flows is developed. The approach furnishes, in effect, a Lagrangian implementation of the compressible Navier–Stokes equations. As the flow proceeds, the mesh is maintained undistorted through continuous and adaptive remeshing of the fluid mass. The principal advantage of the present approach lies in the treatment of boundary conditions at material surfaces such as free boundaries, fluid/fluid or fluid/solid interfaces. In contrast to Eulerian approaches, boundary conditions are enforced at material surfaces ab initio and therefore require no special attention. Consistent tangents are obtained for Lagrangian implicit analysis of a Newtonian fluid flow which may exhibit compressibility effects. The accuracy of the approach is assessed by comparison of the solution for a sloshing problem with existing numerical results and its versatility demonstrated through a simulation of wave breaking. The finite element mesh is maintained undistorted throughout the computation by recourse to frequent and adaptive remeshing © 1998 John Wiley & Sons, Ltd.

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Lagrangian finite element analysis of Newtonian fluid flows

Radovitzky

Ortiz

1998

Int. J. Numer. Meth. Engng.

View full text Add to dashboard Cite

A fully Lagrangian ÿnite element method for the analysis of Newtonian ows is developed. The approach furnishes, in e ect, a Lagrangian implementation of the compressible Navier-Stokes equations. As the ow proceeds, the mesh is maintained undistorted through continuous and adaptive remeshing of the uid mass. The principal advantage of the present approach lies in the treatment of boundary conditions at material surfaces such as free boundaries, uid= uid or uid=solid interfaces. In contrast to Eulerian approaches, boundary conditions are enforced at material surfaces ab initio and therefore require no special attention. Consistent tangents are obtained for Lagrangian implicit analysis of a Newtonian uid ow which may exhibit compressibility e ects. The accuracy of the approach is assessed by comparison of the solution for a sloshing problem with existing numerical results and its versatility demonstrated through a simulation of wave breaking. The ÿnite element mesh is maintained undistorted throughout the computation by recourse to frequent and adaptive remeshing ? 1998 John Wiley & Sons, Ltd.

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Numerical modeling of wave breaking induced by fixed or moving boundaries

Cited by 94 publications

References 20 publications

Simulation of floating structure dynamics in waves by implicit coupling of a fully non-linear potential flow model and a rigid body motion approach

Simulation of floating structure dynamics in waves by implicit coupling of a fully non-linear potential flow model and a rigid body motion approach

Lagrangian finite element analysis of Newtonian fluid flows

Lagrangian finite element analysis of Newtonian fluid flows

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