High order ADER schemes for continuum mechanics

S Busto, S Chiocchetti, M Dumbser, E Gaburro… - Frontiers in …, 2020 - frontiersin.org
In this paper we first review the development of high order ADER finite volume and ADER
discontinuous Galerkin schemes on fixed and moving meshes, since their introduction in …

Non-linear shallow water flow modelling over topography with depth-averaged potential equations

O Castro-Orgaz, FN Cantero-Chinchilla - Environmental Fluid Mechanics, 2020 - Springer
Hunter Rouse was the father of the Fluid Mechanics of Open Channel Flow. In this review
article the fundamental advances on the non-hydrostatic modeling of shallow open channel …

A rapid numerical method for solving Serre–Green–Naghdi equations describing long free surface gravity waves

N Favrie, S Gavrilyuk - Nonlinearity, 2017 - iopscience.iop.org
A new numerical method for solving the Serre–Green–Naghdi (SGN) equations describing
dispersive waves on shallow water is proposed. From the mathematical point of view, the …

[BOOK][B] Shallow water hydraulics

O Castro-Orgaz, WH Hager - 2019 - Springer
The purpose of Shallow Water Hydraulics is to present the theory and the computation of
open channel flows using analytical, numerical, and experimental results. The book's target …

Perfectly matched layers methods for mixed hyperbolic–dispersive equations

C Besse, S Gavrilyuk, M Kazakova, P Noble - Water Waves, 2022 - Springer
Absorbing boundary conditions are important when one simulates the propagation of waves
on a bounded numerical domain without creating artificial reflections. In this paper, we …

[PDF][PDF] A robust and rapid numerical method for dispersive models admitting a lagrangian: application to Serre-Green-Naghdi equations for long free surface gravity …

N Favrie, S Gavrilyuk - preprint, 2016 - researchgate.net
A new numerical method for solving the Serre-Green-Naghdi (SGN) equations describing
dispersive waves on shallow water is proposed. From the mathematical point of view, the …

A strategy to implement Dirichlet boundary conditions in the context of ADER finite volume schemes. One-dimensional conservation laws

GI Montecinos - Computers & Fluids, 2016 - Elsevier
ADER schemes are numerical methods, which can reach an arbitrary order of accuracy in
both space and time. They are based on a reconstruction procedure and the solution of …

Numerical Modeling of Non-hydrostatic Free Surface Flow s

O Castro-Orgaz, WH Hager, O Castro-Orgaz… - Shallow Water …, 2019 - Springer
The shallow water equations (SWE) are a dispersionless system of hyperbolic PDEs
obtained by assuming that the vertical flow acceleration is negligible. Under this assumption …

Une méthode numérique robuste et rapide pour la résolution des équations de Serre-Green-Naghdi décrivant les ondes de surfaces de grandes longueurs d'ondes

N Favrie, S Gavrilyuk - CFM 2017-23ème Congrès Français de …, 2017 - hal.science
Une nouvelle méthode numérique pour la résolution des équations de Serre-Green-Naghdi
(SGN) décrivant les ondes dispersives pour les écoulements en eau peu profonde est …