17 research outputs found
Boussinesq systems in two space dimensions over a variable bottom for the generation and propagation of tsunami waves
Considered here are Boussinesq systems of equations of surface water wave
theory over a variable bottom. A simplified such Boussinesq system is derived
and solved numerically by the standard Galerkin-finite element method. We study
by numerical means the generation of tsunami waves due to bottom deformation
and we compare the results with analytical solutions of the linearized Euler
equations. Moreover, we study tsunami wave propagation in the case of the Java
2006 event, comparing the results of the Boussinesq model with those produced
by the finite difference code MOST, that solves the shallow water wave
equations
Generation of two-dimensional water waves by moving bottom disturbances
We investigate the potential and limitations of the wave generation by
disturbances moving at the bottom. More precisely, we assume that the wavemaker
is composed of an underwater object of a given shape which can be displaced
according to a prescribed trajectory. We address the practical question of
computing the wavemaker shape and trajectory generating a wave with prescribed
characteristics. For the sake of simplicity we model the hydrodynamics by a
generalized forced Benjamin-Bona-Mahony (BBM) equation. This practical problem
is reformulated as a constrained nonlinear optimization problem. Additional
constraints are imposed in order to fulfill various practical design
requirements. Finally, we present some numerical results in order to
demonstrate the feasibility and performance of the proposed methodology.Comment: 21 pages, 7 figures, 1 table, 69 references. Other author's papers
can be downloaded at http://www.denys-dutykh.com
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
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
Finite volume and pseudo-spectral schemes for the fully nonlinear 1D Serre equations
After we derive the Serre system of equations of water wave theory from a
generalized variational principle, we present some of its structural
properties. We also propose a robust and accurate finite volume scheme to solve
these equations in one horizontal dimension. The numerical discretization is
validated by comparisons with analytical, experimental data or other numerical
solutions obtained by a highly accurate pseudo-spectral method.Comment: 28 pages, 16 figures, 75 references. Other author's papers can be
downloaded at http://www.denys-dutykh.com
On the use of finite fault solution for tsunami generation problems
The present study is devoted to the problem of tsunami wave generation. The
main goal of this work is two-fold. First of all, we propose a simple and
computationally inexpensive model for the description of the sea bed
displacement during an underwater earthquake, based on the finite fault
solution for the slip distribution under some assumptions on the dynamics of
the rupturing process. Once the bottom motion is reconstructed, we study waves
induced on the free surface of the ocean. For this purpose we consider three
different models approximating the Euler equations of the water wave theory.
Namely, we use the linearized Euler equations (we are in fact solving the
Cauchy-Poisson problem), a Boussinesq system and a novel weakly nonlinear
model. An intercomparison of these approaches is performed. The developments of
the present study are illustrated on the 17 July 2006 Java event, where an
underwater earthquake of magnitude 7.7 generated a tsunami that inundated the
southern coast of Java.Comment: 31 pages, 10 figures, 3 tables. Other author's papers can be
downloaded at http://www.lama.univ-savoie.fr/~dutykh