Wave generation by a moving boundary

Bona, Jerry L.; Varlamov, V V

doi:10.1090/conm/371/06847

Cited by 6 publications

(2 citation statements)

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“…We remind that the current work is motivated by many people's work, (see [5], [7], [8], [10], [11] and [12]), there are also many further references in the works just cited.…”

Section: Hongqiu Chenmentioning

confidence: 99%

Well-posedness for a higher-order, nonlinear, dispersive equation on a quarter plane

Chen¹

2018

Discrete &Amp; Continuous Dynamical Systems - A

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The focus of the current paper is the higher order nonlinear dispersive equation which models unidirectional propagation of small amplitude long waves in dispersive media. The specific interest is in the initial-boundary value problem where spatial variable lies in R + , namely, quarter plane problem. With proper requirement on initial and boundary condition, we show local and global well posedness.

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“…We remind that the current work is motivated by many people's work, (see [5], [7], [8], [10], [11] and [12]), there are also many further references in the works just cited.…”

Section: Hongqiu Chenmentioning

confidence: 99%

Well-posedness for a higher-order, nonlinear, dispersive equation on a quarter plane

Chen¹

2018

Discrete &Amp; Continuous Dynamical Systems - A

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“…There are some classes of problems, which cannot be solved, in principle, with a fixed grid. To give an example, we can mention the class of problems involving moving boundaries such as free surface flows [57][58][59].…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Conservation Laws with Moving Grid Nodes: Application to Tsunami Wave Modelling

et al. 2019

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In the present article, we describe a few simple and efficient finite volume type schemes on moving grids in one spatial dimension combined with an appropriate predictor–corrector method to achieve higher resolutions. The underlying finite volume scheme is conservative, and it is accurate up to the second order in space. The main novelty consists in the motion of the grid. This new dynamic aspect can be used to resolve better the areas with large solution gradients or any other special features. No interpolation procedure is employed; thus, unnecessary solution smearing is avoided, and therefore, our method enjoys excellent conservation properties. The resulting grid is completely redistributed according to the choice of the so-called monitor function. Several more or less universal choices of the monitor function are provided. Finally, the performance of the proposed algorithm is illustrated on several examples stemming from the simple linear advection to the simulation of complex shallow water waves. The exact well-balanced property is proven. We believe that the techniques described in our paper can be beneficially used to model tsunami wave propagation and run-up.

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Higher-Order Hamiltonian Model for Unidirectional Water Waves

Bona

Carvajal²,

Panthee

et al. 2017

J Nonlinear Sci

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Abstract. Formally second-order correct, mathematical descriptions of long-crested water waves propagating mainly in one direction are derived. These equations are analogous to the first-order approximations of KdV-or BBM-type. The advantage of these more complex equations is that their solutions corresponding to physically relevant initial perturbations of the rest state may be accurate on a much longer time scale. The initial-value problem for the class of equations that emerges from our derivation is then considered. A local wellposedness theory is straightforwardly established by way of a contraction mapping argument.A subclass of these equations possess a special Hamiltonian structure that implies the local theory can be continued indefinitely.

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Wave generation by a moving boundary

Cited by 6 publications

References 0 publications

Well-posedness for a higher-order, nonlinear, dispersive equation on a quarter plane

Well-posedness for a higher-order, nonlinear, dispersive equation on a quarter plane

Numerical Simulation of Conservation Laws with Moving Grid Nodes: Application to Tsunami Wave Modelling

Higher-Order Hamiltonian Model for Unidirectional Water Waves

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