11,112 research outputs found
Bottom changes in coastal areas with complex shorelines
A model for the sea-bottom change simulations in coastal areas with complex shorelines is proposed. In deep and intermediate water depths, the hydrodynamic quantities are calculated by numerically integrating the contravariant Boussinesq equations, devoid of Christoffel symbols. In the surf zone, the propagation of the breaking waves is simulated by the nonlinear shallow water equations. The momentum equation is solved inside the turbulent boundary layer in order to calculate intrawave hydrodynamic quantities. An integral formulation for the contravariant suspended sediment advection-diffusion equation is proposed and used for the sea-bottom dynamic simulations. The proposed model is applied to the real case study of Pescara harbor (in Italy)
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
A modified Galerkin/finite element method for the numerical solution of the Serre-Green-Naghdi system
A new modified Galerkin / Finite Element Method is proposed for the numerical
solution of the fully nonlinear shallow water wave equations. The new numerical
method allows the use of low-order Lagrange finite element spaces, despite the
fact that the system contains third order spatial partial derivatives for the
depth averaged velocity of the fluid. After studying the efficacy and the
conservation properties of the new numerical method, we proceed with the
validation of the new numerical model and boundary conditions by comparing the
numerical solutions with laboratory experiments and with available theoretical
asymptotic results
Boussinesq/Boussinesq systems for internal waves with a free surface, and the KdV approximation
We study here some asymptotic models for the propagation of internal and
surface waves in a two-fluid system. We focus on the so-called long wave regime
for one dimensional waves, and consider the case of a flat bottom. Starting
from the classical Boussinesq/Boussinesq system, we introduce a new family of
equivalent symmetric hyperbolic systems. We study the well-posedness of such
systems, and the asymptotic convergence of their solutions towards solutions of
the full Euler system. Then, we provide a rigorous justification of the
so-called KdV approximation, stating that any bounded solution of the full
Euler system can be decomposed into four propagating waves, each of them being
well approximated by the solutions of uncoupled Korteweg-de Vries equations.
Our method also applies for models with the rigid lid assumption, and the
precise behavior of the KdV approximations depending on the depth and density
ratios is discussed for both rigid lid and free surface configurations. The
fact that we obtain {\it simultaneously} the four KdV equations allows us to
study extensively the influence of the rigid lid assumption on the evolution of
the interface, and therefore its domain of validity. Finally, solutions of the
Boussinesq/Boussinesq systems and the KdV approximation are rigorously compared
and numerically computed.Comment: To appear in M2A
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