相关论文: An all-regime and well-balanced Lagrange-projectio…

This work focuses on the numerical approximation of the Shallow Water Equations (SWE) using a Lagrange-Projection type approach. We propose to extend to this context recent implicit-explicit schemes developed in the framework of…

The present work is devoted to the derivation of a fully well-balanced and positivepreserving numerical scheme for the shallow water equations with Coriolis force. The first main issue consists in preserving all the steady states, including…

We formulate a general criterion for the exact preservation of the "lake at rest" solution in general mesh-based and meshless numerical schemes for the strong form of the shallow-water equations with bottom topography. The main idea is a…

This note aims at demonstrating the advantage of moving-water well-balanced schemes over still-water well-balanced schemes for the shallow water equations. We concentrate on numerical examples with solutions near a moving-water equilibrium.…

In this paper we propose a novel second-order accurate well balanced scheme for shallow water equations in general covariant coordinates over manifolds. In our approach, once the gravitational field is defined for the specific case, one…

We develop a two-dimensional high-order numerical scheme that exactly preserves and captures the moving steady states of the shallow water equations with topography or Manning friction. The high-order accuracy relies on a suitable…

The present work focuses on the numerical approximation of the weak solutions of the shallow water model over a non-flat topography. In particular, we pay close attention to steady solutions with nonzero velocity. The goal of this work is…

When dealing with shallow water simulations, the velocity profile is often assumed to be constant along the vertical axis. However, since in many applications this is not the case, modeling errors can be significant. Hence, in this work, we…

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…

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…

We present a first order scheme based on a staggered grid for the shallow water equations with topography in two space dimensions, which enjoys several properties: positivity of the water height, preservation of constant states, and weak…

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…

Many numerical schemes for hyperbolic systems require a piecewise polynomial reconstruction of the cell averaged values, and to simulate perturbed steady states accurately we require a so called 'well balanced' reconstruction scheme. For…

A high-order, well-balanced, positivity-preserving quasi-Lagrange moving mesh DG method is presented for the shallow water equations with non-flat bottom topography. The well-balance property is crucial to the ability of a scheme to…

This paper develops the structure-preserving finite volume weighted essentially non-oscillatory (WENO) hybrid schemes for the shallow water equations under the arbitrary Lagrangian-Eulerian (ALE) framework, dubbed as ALE-WENO schemes. The…

We develop a new finite volume method using unstructured mesh-vertex grids for coupled systems modeling shallow water flows and solute transport over complex bottom topography. Novel well-balanced positivity preserving discretization…

We design and analyse an energy stable, structure preserving and well-balanced scheme for the Ripa system of shallow water equations. The energy stability of the numerical solutions is achieved by introducing appropriate stabilisation terms…

We present an explicit scheme for a two-dimensional multilayer shallow water model with density stratification, for general meshes and collocated variables. The proposed strategy is based on a regularized model where the transport velocity…

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…

We present an adaptive well-balanced positivity preserving central-upwind scheme on quadtree grids for shallow water equations. The use of quadtree grids results in a robust, efficient and highly accurate numerical method. The quadtree…