1,428 research outputs found
Contravariant Boussinesq equations for the simulation of wave transformation, breaking and run-up
We propose an integral form of the fully non-linear Boussinesq equations in
contravariant formulation, in which Christoffel symbols are avoided, in order to
simulate wave transformation phenomena, wave breaking and near shore
currents in computational domains representing the complex morphology of real
coastal regions. The motion equations retain the term related to the
approximation to the second order of the vertical vorticity. A new Upwind
Weighted Essentially Non-Oscillatory scheme for the solution of the fully non-
linear Boussinesq equations on generalised curvilinear coordinate systems is
proposed. The equations are rearranged in order to solve them by a high
resolution hybrid finite volume–finite difference scheme. The conservative part
of the above-mentioned equations, consisting of the convective terms and the
terms related to the free surface elevation, is discretised by a high-order shock-
capturing finite volume scheme; dispersive terms and the term related to the
approximation to the second order of the vertical vorticity are discretised by a
cell-centred finite difference scheme. The shock-capturing method makes it
possible to intrinsically model the wave breaking, therefore no additional terms
are needed to take into account the breaking related energy dissipation in the surf
zone. The model is applied on a real case regarding the simulation of wave fields
and nearshore currents in the coastal region opposite Pescara harbour (Italy)
Finite volume methods for unidirectional dispersive wave models
We extend the framework of the finite volume method to dispersive
unidirectional water wave propagation in one space dimension. In particular we
consider a KdV-BBM type equation. Explicit and IMEX Runge-Kutta type methods
are used for time discretizations. The fully discrete schemes are validated by
direct comparisons to analytic solutions. Invariants conservation properties
are also studied. Main applications include important nonlinear phenomena such
as dispersive shock wave formation, solitary waves and their various
interactions.Comment: 25 pages, 12 figures, 51 references. Other authors papers can be
downloaded at http://www.lama.univ-savoie.fr/~dutykh
A numerical model for the simulation of a solitary wave in a coastal region
In this paper we propose a numerical model for the simulation of the tsunami wave propagation on coastal region. The model can simulate the wave transformation due to refraction, shoaling, diffraction and breaking phenomena that take place in the surf zone and can simulate the wet front progress on the mainland. The above mentioned model is based on the numerical integration of the Fully Non-linear Boussinesq Equations in the deep water region and of the Non-linear Shallow Water Equations in the surf zone. These equations are expressed in an integral contravariant formulation and are integrated on generalized curvilinear boundary conforming grid that can reproduce the complex morphology of the coast line. The numerical integration of the model equations is implemented by a high order Upwind WENO numerical scheme that involves an exact Riemann Solver. For the simulation of the wet front progress on the dry bed, the exact solution of the Riemann problem for the wet-dry front is used. The capacity of the proposed model to simulate the wet front progress velocity is tested by numerical reproducing the dam-break problem on a dry bed. The capacity of the proposed model to correctly simulate the tsunami wave evolution and propagation on the coastal region is tested by numerical reproducing a benchmark test case about the tsunami wave propagation on a conic island
Finite volume schemes for dispersive wave propagation and runup
Finite volume schemes are commonly used to construct approximate solutions to
conservation laws. In this study we extend the framework of the finite volume
methods to dispersive water wave models, in particular to Boussinesq type
systems. We focus mainly on the application of the method to bidirectional
nonlinear, dispersive wave propagation in one space dimension. Special emphasis
is given to important nonlinear phenomena such as solitary waves interactions,
dispersive shock wave formation and the runup of breaking and non-breaking long
waves.Comment: 41 pafes, 20 figures. Other author's papers can be downloaded at
http://www.lama.univ-savoie.fr/~dutykh
A splitting approach for the fully nonlinear and weakly dispersive Green-Naghdi model
The fully nonlinear and weakly dispersive Green-Naghdi model for shallow
water waves of large amplitude is studied. The original model is first recast
under a new formulation more suitable for numerical resolution. An hybrid
finite volume and finite difference splitting approach is then proposed. The
hyperbolic part of the equations is handled with a high-order finite volume
scheme allowing for breaking waves and dry areas. The dispersive part is
treated with a classical finite difference approach. Extensive numerical
validations are then performed in one horizontal dimension, relying both on
analytical solutions and experimental data. The results show that our approach
gives a good account of all the processes of wave transformation in coastal
areas: shoaling, wave breaking and run-up
Finite volume methods for unidirectional dispersive wave model
We extend the framework of the finite volume method to dispersive unidirectional water wave propagation in one space dimension. In particular, we consider a KdV–BBM-type equation. Explicit and implicit–explicit Runge–Kutta-type methods are used for time discretizations. The fully discrete schemes are validated by direct comparisons to analytic solutions. Invariants’ conservation properties are also studied. Main applications include important nonlinear phenomena such as dispersive shock wave formation, solitary waves, and their various interaction
A discontinuous Galerkin method for a new class of Green-Naghdi equations on simplicial unstructured meshes
In this paper, we introduce a discontinuous Finite Element formulation on
simplicial unstructured meshes for the study of free surface flows based on the
fully nonlinear and weakly dispersive Green-Naghdi equations. Working with a
new class of asymptotically equivalent equations, which have a simplified
analytical structure, we consider a decoupling strategy: we approximate the
solutions of the classical shallow water equations supplemented with a source
term globally accounting for the non-hydrostatic effects and we show that this
source term can be computed through the resolution of scalar elliptic
second-order sub-problems. The assets of the proposed discrete formulation are:
(i) the handling of arbitrary unstructured simplicial meshes, (ii) an arbitrary
order of approximation in space, (iii) the exact preservation of the motionless
steady states, (iv) the preservation of the water height positivity, (v) a
simple way to enhance any numerical code based on the nonlinear shallow water
equations. The resulting numerical model is validated through several
benchmarks involving nonlinear wave transformations and run-up over complex
topographies
Numerical simulation of strongly nonlinear and dispersive waves using a Green-Naghdi model
We investigate here the ability of a Green-Naghdi model to reproduce strongly
nonlinear and dispersive wave propagation. We test in particular the behavior
of the new hybrid finite-volume and finite-difference splitting approach
recently developed by the authors and collaborators on the challenging
benchmark of waves propagating over a submerged bar. Such a configuration
requires a model with very good dispersive properties, because of the
high-order harmonics generated by topography-induced nonlinear interactions. We
thus depart from the aforementioned work and choose to use a new Green-Naghdi
system with improved frequency dispersion characteristics. The absence of dry
areas also allows us to improve the treatment of the hyperbolic part of the
equations. This leads to very satisfying results for the demanding benchmarks
under consideration
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