A Multi-Layer Approach to Boussinesq-Type Modeling

Lynett, Patrick; Liu, P. L.-F.; Hwung, H. H.

doi:10.1142/9789812701916_0005

Cited by 6 publications

(11 citation statements)

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“…The numerical results are compared with three-dimensional wave tank laboratory experimental data [28]. Furthermore, the results of the present two horizontal dimensions model is compared with the results of the three-dimensional fully potential model (BIEM) [31] and a two-layer high-order model [26] and in all cases, an excellent agreement has been achieved. For investigating of the effects of nonlinearity and frequency dispersion, the results are compared with available experimental data at several wave gauges that were installed at different distances from impulse wave source.…”

Section: Discussionmentioning

confidence: 79%

“…The results of the present model are also compared with the results of a multi-layer high-accuracy model developed by Lynett and Liu [26] which allows for a higher-order accuracy of O( 2 ) in each layer. The comparison is made in water surface profile along the slide axis and it is considered that the sliding mass is symmetric about the slide axis and the solid sliding block geometry is not changed in width (Y -direction in Figure 1).…”

Section: Comparison With Multi-layer Modelsmentioning

confidence: 99%

“…The comparison is made in water surface profile along the slide axis and it is considered that the sliding mass is symmetric about the slide axis and the solid sliding block geometry is not changed in width (Y -direction in Figure 1). Four data sets which are compared in this section are as follows: (1) the fully potential theory which is used in BIEM model [28], (2) the one-layer second-order approximation which derived by Lynett and Liu [23], (3) the two-layer approach in which, the order of approximation in each layer is O( 2 ) [26], and (4) the present fourth-order approximation O( 4 ). The comparisons of several data sets are made based on the definition of a characteristic water depth ratio as L s / h C (t) where L s is the horizontal length of slide mass and h 0C (t) is the submergence of the sliding block centre of mass which can be changed by mass movement.…”

Section: Comparison With Multi-layer Modelsmentioning

confidence: 99%

See 2 more Smart Citations

A higher‐order Boussinesq‐type model with moving bottom boundary: applications to submarine landslide tsunami waves

Ataie-Ashtiani

Jilani

2006

Numerical Methods in Fluids

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SUMMARYA two-dimensional depth-integrated numerical model is developed using a fourth-order Boussinesq approximation for an arbitrary time-variable bottom boundary and is applied for submarine-landslide-generated waves. The mathematical formulation of model is an extension of (4,4) Padé approximant for moving bottom boundary. The mathematical formulations are derived based on a higher-order perturbation analysis using the expanded form of velocity components. A sixth-order multi-step finite difference method is applied for spatial discretization and a sixth-order Runge-Kutta method is applied for temporal discretization of the higher-order depth-integrated governing equations and boundary conditions. The present model is validated using available three-dimensional experimental data and a good agreement is obtained. Moreover, the present higher-order model is compared with fully potential three-dimensional models as well as Boussinesq-type multi-layer models in several cases and the differences are discussed. The high accuracy of the present numerical model in considering the nonlinearity effects and frequency dispersion of waves is proven particularly for waves generated in intermediate and deeper water area.

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Section: Discussionmentioning

confidence: 79%

Section: Comparison With Multi-layer Modelsmentioning

confidence: 99%

Section: Comparison With Multi-layer Modelsmentioning

confidence: 99%

See 1 more Smart Citation

A higher‐order Boussinesq‐type model with moving bottom boundary: applications to submarine landslide tsunami waves

Ataie-Ashtiani

Jilani

2006

Numerical Methods in Fluids

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“…3) for the R-H7-30-31 test is selected as a standard for the comparison of the numerical and the experimental results in the generation stage (Fig. 5), because its hyperbolic geometry of the sliding mass is the most appropriate simplification of the real landslide geometries (Grilli et al 2002;Lynett and Liu 2004) and the sliding masses are supposed to be rigid in the numerical model. In this comparison, the numerical and experimental results are in rather good agreement.…”

Section: Periods and Amplitudes In Generating Stagementioning

confidence: 99%

Numerical simulation of wave generated by landslide incidents in dam reservoirs

Ataie-Ashtiani

Yavari-Ramshe

2011

Landslides

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In this work, a two-dimensional fourth-order Boussinesqtype numerical model is applied to estimate the impact of landslide-generated waves in dam reservoirs. This numerical model has recently been extended for simulating subaerial landslides. The extended model is validated using available three-dimensional experimental data, and a good agreement is obtained. The numerical model is then employed to investigate the impact of landslide-generated waves in two real cases, the Maku and Shafa-Roud dam reservoirs in the northwestern and the north of Iran, respectively. Generated wave heights, wave run-up, maximum wave height above dam crest, and dam overtopping volume have been estimated for each case. The amplitude of generated waves about 18 and 31m and the volume of dam overtopping up to 80,000m 3 emphasize the importance of the estimation of the landslide-generated waves in dam sites.

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“…A specific quadratic vertical profile yields equivalence to the Serre equations, for which only one scalar in the traditional equation system needs to be modified. Other attempts include viscosity into the equations [11] or use Boussinesq-type equations for multiple layers [15,16]. In case of constant bathymetries, the non-hydrostatic extension is another way to circumvent mixed space-time derivatives arising in Boussinesq-type equations.…”

mentioning

confidence: 99%

Depth‐averaged non‐hydrostatic extension for shallow water equations with quadratic vertical pressure profile: equivalence to Boussinesq‐type equations

Jeschke

Pedersen

Vater

et al. 2017

Numerical Methods in Fluids

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Summary We reformulate the depth‐averaged non‐hydrostatic extension for shallow water equations to show equivalence with well‐known Boussinesq‐type equations. For this purpose, we introduce two scalars representing the vertical profile of the non‐hydrostatic pressure. A specific quadratic vertical profile yields equivalence to the Serre equations, for which only one scalar in the traditional equation system needs to be modified. Equivalence can also be demonstrated with other Boussinesq‐type equations from the literature when considering variable depth, but then the non‐hydrostatic extension involves mixed space–time derivatives. In case of constant bathymetries, the non‐hydrostatic extension is another way to circumvent mixed space–time derivatives arising in Boussinesq‐type equations. On the other hand, we show that there is no equivalence when using the traditionally assumed linear vertical pressure profile. Linear dispersion and asymptotic analysis as well as numerical test cases show the advantages of the quadratic compared with the linear vertical non‐hydrostatic pressure profile in the depth‐averaged non‐hydrostatic extension for shallow water equations. Copyright © 2017 John Wiley & Sons, Ltd.

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A Multi-Layer Approach to Boussinesq-Type Modeling

Cited by 6 publications

References 0 publications

A higher‐order Boussinesq‐type model with moving bottom boundary: applications to submarine landslide tsunami waves

A higher‐order Boussinesq‐type model with moving bottom boundary: applications to submarine landslide tsunami waves

Numerical simulation of wave generated by landslide incidents in dam reservoirs

Depth‐averaged non‐hydrostatic extension for shallow water equations with quadratic vertical pressure profile: equivalence to Boussinesq‐type equations

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