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Well-balanced central schemes for two-dimensional systems of shallow water equations with wet and dry states

机译:具有干态和湿态的二维浅水方程组的均衡中心方案

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The aim of this paper is to develop a new second-order accurate central scheme for the numerical solution of the two-dimensional system of shallow water equations (SWE) featuring wet and dry states over variable waterbeds. The proposed central scheme follows a classical Riemann-free finite volume method and evolves the numerical solution of systems of hyperbolic balance laws on a single Cartesian grid. Furthermore, the proposed well-balanced scheme preserves the lake at rest constraint thanks to a careful well-balanced discretization of the SWE system, and allows a proper interaction between wet and dry states whenever water run-ups/drains arise. For verification purposes, classical SWE problems appearing in the recent literature are successfully solved.
机译:本文的目的是为具有可变水床上干湿状态的浅水方程组(SWE)二维系统的数值解开发一种新的二阶精确中心格式。所提出的中心方案遵循经典的无Riemann有限体积方法,并且在单个笛卡尔网格上发展了双曲平衡定律系统的数值解。此外,由于对SWE系统进行了精心均衡的离散化处理,因此拟议的均衡方案可保护湖泊在静止状态下的约束,并且每当水量增加/雨水出现时,湿态和干态之间便会发生适当的相互作用。为了验证,成功解决了最近文献中出现的经典SWE问题。

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