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We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…

Numerical Analysis · Mathematics 2021-05-27 Cecilia Pagliantini

In this technical report we compare different deep learning models for prediction of water depth rasters at high spatial resolution. Efficient, accurate, and fast methods for water depth prediction are nowadays important as urban floods are…

We are interested in asymptotic models for the propagation of internal waves at the interface between two shallow layers of immiscible fluid, under the rigid-lid assumption. We review and complete existing works in the literature, in order…

Analysis of PDEs · Mathematics 2021-11-18 Vincent Duchene , Samer Israwi , Raafat Talhouk

In this study, we investigate the Shallow Water Equations incorporating source terms accounting for Manning friction and a non-flat bottom topology. Our primary focus is on developing and validating numerical schemes that serve a dual…

Numerical Analysis · Mathematics 2023-10-24 Guanlan Huang , Sebastiano Boscarino , Tao Xiong

The paper proposes a new, conservative fully-discrete scheme for the numerical solution of the regularised shallow water Boussinesq system of equations in the cases of periodic and reflective boundary conditions. The particular system is…

Numerical Analysis · Mathematics 2021-05-12 Dimitrios Mitsotakis , Hendrik Ranocha , David I. Ketcheson , Endre Süli

In this paper, we consider the Kakutani-Matsuuchi model which describes the surface elevation of the water-waves under the effect of viscosity. We show wave breaking for the Kakutani-Matsuuchi model, namely, the solution remains bounded but…

Analysis of PDEs · Mathematics 2023-05-02 Shaojie Yang , Jianmin Zhao

Two-dimensional free-surface potential flows of an ideal fluid over a strongly inhomogeneous bottom are investigated with the help of conformal mappings. Weakly-nonlinear and exact nonlinear equations of motion are derived by the…

Fluid Dynamics · Physics 2016-09-08 V. P. Ruban

In this paper, we study the motion of the free surface of a body of fluid over a variable bottom, in a long wave asymptotic regime. We assume that the bottom of the fluid region can be described by a stationary random process $\beta(x,…

Analysis of PDEs · Mathematics 2009-11-13 Anne de Bouard , Walter Craig , Oliver Díaz-Espinosa , Philippe Guyenne , Catherine Sulem

Existing theoretical results for attenuation of surface waves propagating on water of random fluctuating depth are shown to over predict the rate of decay due to the way in which ensemble averaging is performed. A revised approach is…

Fluid Dynamics · Physics 2026-03-05 Lloyd Dafydd , Richard Porter

A rigid body model for the dynamics of a marine vessel, used in simulations of offshore pipe-lay operations, gives rise to a set of ordinary differential equations with controls. The system is input-output passive. We propose…

Numerical Analysis · Mathematics 2018-04-24 Elena Celledoni , Eirik Hoel Høiseth , Nataliya Ramzina

In this paper, we review the history and current state-of-the-art in the modelling of long nonlinear dispersive waves. For the sake of conciseness of this review, we omit the unidirectional models and focus especially on some classical and…

Fluid Dynamics · Physics 2020-02-20 Gayaz Khakimzyanov , Denys Dutykh , Zinaida Fedotova , Dimitrios Mitsotakis

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…

Atmospheric and Oceanic Physics · Physics 2010-04-22 Florent Chazel , David Lannes , Fabien Marche

This paper is devoted to the asymptotic analysis of strongly rotating and stratified fluids, under a $\beta$-plane approximation, and within a three-dimensional spatial domain with strong topography. Our purpose is to propose a linear…

Analysis of PDEs · Mathematics 2026-01-06 Anne-Laure Dalibard , Corentin Gentil

We present a discontinuous finite element method for the shallow water equations which exploits high-resolution realistic bathymetry data without any regularity assumption, also in the case of high-order discretizations. We prove a number…

Computational Engineering, Finance, and Science · Computer Science 2026-05-21 Luca Arpaia , Giuseppe Orlando , Christian Ferrarin , Luca Bonaventura

A high-frequency recovered fully discrete low-regularity integrator is constructed to approximate rough and possibly discontinuous solutions of the semilinear wave equation. The proposed method, with high-frequency recovery techniques, can…

Numerical Analysis · Mathematics 2024-10-18 Jiachuan Cao , Buyang Li , Yanping Lin , Fangyan Yao

In this paper a three-parameter family of Boussinesq systems is studied. The systems have been proposed as models of the propagation of long internal waves along the interface of a two-layer system of fluids with rigid-lid condition for the…

Numerical Analysis · Mathematics 2021-10-27 V. A. Dougalis , A. Duran , L. Saridaki

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…

Classical Physics · Physics 2020-01-09 Denys Dutykh , Theodoros Katsaounis , Dimitrios Mitsotakis

In this study, we focus on the modelling of coupled systems of shallow water flows and solute transport with source terms due to variable topography and friction effect. Our aim is to propose efficient and accurate numerical techniques for…

Numerical Analysis · Mathematics 2021-10-12 Amine Hanini , Abdelaziz Beljadid , Driss Ouazar

We rigorously justify in 3D the main asymptotic models used in coastal oceanography, including: shallow-water equations, Boussinesq systems, Kadomtsev-Petviashvili (KP) approximation, Green-Naghdi equations, Serre approximation and…

Analysis of PDEs · Mathematics 2016-03-08 Borys Alvarez-Samaniego , David Lannes

3D particle tracking velocimetry (PTV) is a key technique for analyzing turbulent flow, one of the most challenging computational problems of our century. At the core of 3D PTV is the dual-frame fluid motion estimation algorithm, which…

Computer Vision and Pattern Recognition · Computer Science 2024-10-17 Yifei Zhang , Huan-ang Gao , Zhou Jiang , Hao Zhao