Well‐balanced nonstaggered central schemes based on hydrostatic reconstruction for the shallow water equations with Coriolis forces and topography

2020 ◽  
Vol 44 (2) ◽  
pp. 1358-1376
Author(s):  
Jian Dong ◽  
Ding Fang Li
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Coriolis Forces ◽  
Central Schemes

Well-balanced schemes for the shallow water equations with Coriolis forces

2017 ◽  
Vol 138 (4) ◽  
pp. 939-973 ◽  
Author(s):  
Alina Chertock ◽  
Michael Dudzinski ◽  
Alexander Kurganov ◽  
Mária Lukáčová-Medvid’ová
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Coriolis Forces

scholarly journals Finite-volume schemes for shallow-water equations

Acta Numerica ◽  
2018 ◽  
Vol 27 ◽  
pp. 289-351 ◽  
Author(s):  
Alexander Kurganov
Keyword(s):  
Shallow Water ◽  
Finite Volume ◽  
Shallow Water Equations ◽  
Hyperbolic Systems ◽  
Bottom Topography ◽  
Water System ◽  
Problem Solver ◽  
Finite Volume Schemes ◽  
Upwind Schemes ◽  
Central Schemes

Shallow-water equations are widely used to model water flow in rivers, lakes, reservoirs, coastal areas, and other situations in which the water depth is much smaller than the horizontal length scale of motion. The classical shallow-water equations, the Saint-Venant system, were originally proposed about 150 years ago and still are used in a variety of applications. For many practical purposes, it is extremely important to have an accurate, efficient and robust numerical solver for the Saint-Venant system and related models. As their solutions are typically non-smooth and even discontinuous, finite-volume schemes are among the most popular tools. In this paper, we review such schemes and focus on one of the simplest (yet highly accurate and robust) methods: central-upwind schemes. These schemes belong to the family of Godunov-type Riemann-problem-solver-free central schemes, but incorporate some upwinding information about the local speeds of propagation, which helps to reduce an excessive amount of numerical diffusion typically present in classical (staggered) non-oscillatory central schemes. Besides the classical one- and two-dimensional Saint-Venant systems, we will consider the shallow-water equations with friction terms, models with moving bottom topography, the two-layer shallow-water system as well as general non-conservative hyperbolic systems.

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