Time-Dependent Numerical Code for Extended Boussinesq Equations

Wei, Guojian; Kirby, James T.

doi:10.1061/(asce)0733-950x(1995)121:5(251)

Cited by 462 publications

(324 citation statements)

References 17 publications

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“…We enforce periodic waves generation with the use of a generation/relaxation zone, following [50]. We have implemented the relaxation functions proposed in [75] and at the inlet boundary, we progressively impose on a two-wavelength long generation layer the targeted wave train.…”

Section: Boundary Conditionsmentioning

confidence: 99%

“…A large number of numerical methods have been developed in the past few years for the BT equations. Let us mention for instance some Finite-Difference (FDM in the following) approaches [49,54,65,75], Finite-Element methods (FEM in the following) [46,59,66,73], Finite-Volume discretizations (FVM in the following) for 1d equations [21], hybrid FDM / FVM [24,25,55,64,69], or even a purely 2d FVM discretization on unstructured recently been performed in [43]. Let us also mention [10] and more recently [63] for a 2D cartesian numerical model based on fully non-linear BT equations of [76].…”

Section: Introductionmentioning

confidence: 99%

“…A large number of numerical methods have been developed in the past few years for the BT equations. Let us mention for instance some Finite-Difference (FDM in the following) approaches [49,54,65,75] As far as flexibility is concerned, the use of discontinuous-Galerkin methods (dG methods in the following) would appear as a natural choice. Indeed, this class of method provides several appealing features, like compact discretization stencils and hp-adaptivity, flexibility with a natural handling of unstructured meshes, easy parallel computation and local conservation properties in the approximation of conservation laws.…”

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confidence: 99%

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Discontinuous-Galerkin Discretization of a New Class of Green-Naghdi Equations

Duran

Marche

2015

Commun. Comput. Phys.

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Abstract. We describe in this work a discontinuous-Galerkin Finite-Element method to approximate the solutions of a new family of 1d Green-Naghdi models. These new models are shown to be more computationally efficient, while being asymptotically equivalent to the initial formulation with regard to the shallowness parameter. Using the free surface instead of the water height as a conservative variable, the models are recasted under a pre-balanced formulation and discretized using an expansion basis of arbitrary order. Independently from the polynomial degree in the approximation space, the preservation of the motionless steady-states is automatically ensured, and the water height positivity is enforced. A simple numerical procedure devoted to handle broken waves is also described. The validity of the resulting model is assessed through extensive numerical validations.. . IntroductionDepth-averaged equations are widely used in coastal engineering for the simulation of nonlinear waves propagation and transformations in nearshore areas. The full description of surface water waves in an incompressible, homogeneous, inviscid fluid, is provided by the free surface Euler (or water waves) equations but this problem remains mathematically and numerically challenging. As a consequence, the use of depth averaged equations helps to reduce the three-dimensional problem to a two-dimensional problem, while keeping a good level of accuracy in many configurations. Many Boussinesq-like models are used nowadays and a detailed review can be found in [42] and the recent monograph [41]. Denoting by λ the typical horizontal scale of the flow and h 0 the typical depth, the shallow water regime usually corresponds to the configuration where µ := [52,54,57] for instance, an additional smallness amplitude assumption on the typical wave amplitude a is classically performed: ε := a h0 = O(µ). This assumption often appears as too restrictive for many applications in coastal oceanography. Removing the small amplitude assumption while still keeping all the O(µ) terms, we obtain the so-called Green-Naghdi equations (GN equations in the following) [34], also referred to as Serre equations [62] or fully non-linear Boussinesq equations [76]. A large number of numerical methods have been developed in the past few years for the BT equations. Let us mention for instance some Finite-Difference (FDM in the following) approaches [49,54,65,75] As far as flexibility is concerned, the use of discontinuous-Galerkin methods (dG methods in the following) would appear as a natural choice. Indeed, this class of method provides several appealing features, like compact discretization stencils and hp-adaptivity, flexibility with a natural handling of unstructured meshes, easy parallel computation and local conservation properties in the approximation of conservation laws. A general review of dG methods for convection dominated problems is performed in [14]. Concerning the approximation of more general problems, involving higher-order derivatives, several methods a...

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Section: Boundary Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…A large number of numerical methods have been developed in the past few years for the BT equations. Let us mention for instance some Finite-Difference (FDM in the following) approaches [49,54,65,75] As far as flexibility is concerned, the use of discontinuous-Galerkin methods (dG methods in the following) would appear as a natural choice. Indeed, this class of method provides several appealing features, like compact discretization stencils and hp-adaptivity, flexibility with a natural handling of unstructured meshes, easy parallel computation and local conservation properties in the approximation of conservation laws.…”

mentioning

confidence: 99%

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Discontinuous-Galerkin Discretization of a New Class of Green-Naghdi Equations

Duran

Marche

2015

Commun. Comput. Phys.

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“…The added mass and damping coefficients are obtained from a pre-computed hydrodynamic file as prepared with Wavescat. The wave forcing is obtained from the results of available wave simulations at the berth with Funwave [16] from MetOcean Solutions [17,18]. The incident short wave frequency spectra were obtained from the time series of surface elevations.…”

Section: Quaysimmentioning

confidence: 99%

Improvement of Mooring Configurations in Geraldton Harbour

Molen

Scott

Taylor

et al. 2015

JMSE

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Ports exposed to high energy long wave conditions can experience significantly reduced berth operability. Geraldton is perhaps one of the best known examples. Recent studies to mitigate the problems have concentrated on the reduction of the long waves by extending the breakwater. However, this is quite costly. Various countermeasures related to the mooring configuration are defined and analysed in this paper. The analysed alternatives are use of shore-based mooring lines, installation of softer fenders, a combination of these two, and deployment of Cavotec MoorMaster™ units. These alternatives were compared with the existing mooring configuration and with the option to extend the breakwater. The best improvement (50% increase of threshold long wave height inside the harbour) is reached by installing a combination of pneumatic fenders and constant tension winches set to 30 t, or nylon breast lines on a brake winch with a pretension of 25 t. In this way, the vessel is pulled into the fenders and fender friction prevents excessive surging of the ship along the berth.

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“…Several studies have presented numerical wave tanks based on boundary integral equations (Isaacson 1982;Kim, Liu, & Ligget, 1983;Longuet-Higgins & Cokelet, 1976) and Boussinesq equations (Nwogu, 1993;Wei & Kirby, 1995). The numerical wave tanks based on boundary integral equations are limited in their application due to being single phase and due to the assumption of the irrotational flow.…”

Section: Introductionmentioning

confidence: 99%

Evaluating wave forces on groups of three and nine cylinders using a 3D numerical wave tank

Kamath

Chella

Bihs

et al. 2015

Engineering Applications of Computational Fluid Mechanics

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The evaluation of the complex wave regime due to wave interaction with a large group of cylinders placed in proximity requires an efficient and accurate numerical model. This paper presents the application of a two-phase Computational Fluid Dynamics (CFD) model to carry out a detailed investigation of wave forces and flow around vertical circular cylinders placed in groups of different configurations at low Keulegan-Carpenter (KC) numbers. The 3D numerical wave tank is validated by comparing the numerical results with experimental data. Further, the hydrodynamic effects associated with three cylinders placed in tandem, side by side and in a 3 × 3 square array of nine cylinders are investigated. Wave forces are seen to reduce along the row in a tandem array. In a side-by-side arrangement, the central cylinder experiences the highest force. A combination of these effects is seen in the 3 × 3 square array. The variation of the wave forces on the cylinders in the array for different center-to-center distances and incident wavelengths is evaluated and the results show that the wave forces are the highest on the cylinders when the center-to-center distance is slightly less than half the incident wavelength.

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Time-Dependent Numerical Code for Extended Boussinesq Equations

Cited by 462 publications

References 17 publications

Discontinuous-Galerkin Discretization of a New Class of Green-Naghdi Equations

Discontinuous-Galerkin Discretization of a New Class of Green-Naghdi Equations

Improvement of Mooring Configurations in Geraldton Harbour

Evaluating wave forces on groups of three and nine cylinders using a 3D numerical wave tank

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