Related papers: A fully well-balanced scheme for shallow water equ…
In this work, the exact reproduction of a moving-water steady flow via the numerical solution of the one-dimensional shallow water equations is studied. A new scheme based on a modified version of the HLLEM approximate Riemann solver…
We develop a well-balanced central-upwind scheme for rotating shallow water model with horizontal temperature and/or density gradients---the thermal rotating shallow water (TRSW). The scheme is designed using the flux globalization…
We consider in this work the numerical resolution of a 2D shallow water system with a Coriolis effect and bottom friction stresses on unstructured meshes by a new Finite Volume Characteristics (FVC) scheme, which has been introduced in the…
In this work, we present a high-order finite volume framework for the numerical simulation of shallow water flows. The method is designed to accurately capture complex dynamics inherent in shallow water systems, particularly suited for…
The two-dimensional shallow water equations with a particular bottom and the Coriolis's force $f=f_{0}+\Omega y$ are studied in this paper. The main goal of the paper is to describe all invariant solutions for which the reduced system is a…
In this work, we propose a second-order accurate scheme for shallow water equations in general covariant coordinates over manifolds. In particular, the covariant parametrization in general covariant coordinates is induced by the metric…
A quasi-second order scheme is developed to obtain approximate solutions of the shallow water equationswith bathymetry. The scheme is based on a staggered finite volume scheme for the space discretization:the scalar unknowns are located in…
We present well-balanced finite volume schemes designed to approximate the Euler equations with gravitation. They are based on a novel local steady state reconstruction. The schemes preserve a discrete equivalent of steady adiabatic flow,…
In this paper, high order well-balanced finite difference weighted essentially non-oscillatory methods to solve general systems of balance laws are presented. Two different families are introduced: while the methods in the first one…
In this paper, we are concerned with the shallow water flow model over non-flat bottom topography by high-order schemes. Most of the numerical schemes in the literature are developed from the original mathematical model of the shallow water…
In this work, we develop a new hydrostatic reconstruction procedure to construct well-balanced schemes for one and multilayer shallow water flows, including wetting and drying. Initially, we derive the method for a path-conservative finite…
High order finite volume schemes for conservation laws are very useful in applications, due to their ability to compute accurate solutions on quite coarse meshes and with very few restrictions on the kind of cells employed in the…
This paper presents a more stable implementation and a highly accurate numerical tool for predicting flooding in urban areas. We started with the (linearised) well-posedness analysis by [1], where far-field boundary conditions were proposed…
A high-order well-balanced scheme for the Euler equations with gravitation is presented. The scheme is able to preserve a spatially high-order accurate discrete representation of a large class of hydrostatic equilibria. It is based on a…
We compare some first order well-balanced numerical schemes for shallow water system with special interest in applications where there are abrupt variations of the topography. We show that the space step required to obtain a prescribed…
The group properties of the shallow-water equations with the complete Coriolis force is the subject of this study. In particular we apply the Lie theory to classify the system of three nonlinear partial differential equations according to…
In this paper, we propose a new well-balanced fifth-order finite volume WENO method for solving one- and two-dimensional shallow water equations with bottom topography. The well-balanced property is crucial to the ability of a scheme to…
This work investigates the topical problem of balancing the shallow water equations over the bottom steps of different heights. The current approaches in the literature are essentially based on mathematical analysis of the hyperbolic system…
The present work concerns the derivation of a fully well-balanced Godunov-type finite volume scheme for the Euler equations with a gravitational potential based on an approximate Riemann solver in a one-dimensional framework. It is an…
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…