Classical methods of parameter estimation usually imply the minimisation of an objective function, that measures the error between some observations and the results obtained by a numerical model. In the presence of random inputs, the objective function becomes a random variable, and notions of robustness have to be introduced. In this paper, we are...
The aim of this paper is to prove the preservation of the diffusive limit by a numerical scheme for the shallow-water equations with a Manning friction source term. This asymptotic behavior coincides with the long time and stiff friction limit. The adopted discretization was initially developed to preserve all the steady states of the model under c...
A theoretical framework and numerical techniques to solve optimal control problems with a spatial trace term in the terminal cost and governed by regularized nonlinear hyperbolic conservation laws are provided. Depending on the spatial dimension, the set at which the optimum of the trace term is reached under the action of the control function can ...
Published in Ocean Dynamics
We present an idealized network model for storm surges in the Wadden Sea, specifically including a time-dependent wind forcing (wind speed and direction). This extends the classical work by H.A. Lorentz who only considered the equilibrium response to a steady wind forcing. The solutions obtained in the frequency domain for the linearized shallow-wa...
In this communication, we consider a numerical scheme for the shallow-water system. The scheme under consideration has been proven to preserve the positivity of the water height and to be fully well-balanced, i.e. to exactly preserve the moving steady state solutions of the shallow-water equations with the topography source term. The goal of this w...
Published in Natural Hazards
The tsunamis that have occurred in many places around the world over the past decades have taken a heavy toll on human lives and property. The eastern coast of the Korean Peninsula is not safe from tsunamis and has sustained tsunami damage in the past. The aim of this study is to review the past, present, and future of some aspects of tsunami resea...
Understanding salt dynamics is important to adequately model salt intrusion, baroclinic forcing, and sediment transport. In this paper, the importance of the residual salt transport due to tidal advection in well-mixed tidal estuaries is studied. The water motion is resolved in a consistent way with a width-averaged analytical model, coupled to an ...
Published in Bulletin of the Brazilian Mathematical Society, New Series
The present work is focused on the numerical approximation of the shallow water equations. When studying this problem, one faces at least two important issues, namely the ability of the scheme to preserve the positiveness of the water depth, along with the ability to capture the stationary states.We propose here aGodunov-typemethod that fully satis...
This work is devoted to the derivation of a fully well-balanced numerical scheme for the well-known shallow-water model. During the last two decades, several well-balanced strategies have been introduced with a special attention to the exact capture of the stationary states associated with the so-called lake at rest. By fully well-balanced, we mean...
Published in Ocean Dynamics
In this study, a new method of storm surge modeling is proposed. This method is orders of magnitude faster than the traditional method within the linear dynamics framework. The tremendous enhancement of the computational efficiency results from the use of a pre-calculated all-source Green’s function (ASGF), which connects a point of interest (POI) ...
