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A well-balanced spectral volume scheme with the wetting-drying property for the shallow-water equations

机译：浅水方程组具有干湿特性的平衡谱体积方案

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摘要

The shallow-water equations are widely used to model surface water bodies, such as lakes, rivers and the swash zone in coastal flows. Physically congruent solutions are characterized by non-negative water depth, and many numerical methods may fail to preserve this property at the discrete level when moving wet-dry transitions are present in the physical domain, In this paper, we present a spectral-volume method for the approximate solution of the one-dimensional shallow-water equations, which is third-order accurate in wet regions, far from discontinuities, and which is well balanced for water at rest states: the stability of the solution is ensured if reconstruction and limitation of variables preserves non-negativity of the depth and a suitable constraint for the time step length is satisfied. A number of numerical experiments are reported, showing the promising capabilities of the model to solve problems with non-trivial topographies and friction.
机译：浅水方程被广泛用于模拟地表水体，例如沿海水流中的湖泊，河流和冲积带。物理上一致的解决方案的特征在于非负水深，当物理域中出现干湿转换时，许多数值方法可能无法在离散水平上保留此特性。在本文中，我们提出了一种频谱量方法一维浅水方程的近似解，在潮湿区域三阶精确，没有不连续性，并且对于静止状态下的水具有很好的平衡：如果重构和限制，则可以确保解的稳定性变量保留了深度的非负值，并且满足了对时间步长的适当限制。报告了许多数值实验，显示了该模型解决非平凡地形和摩擦问题的有前途的功能。

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  • 来源
    《Journal of Hydroinformatics》 |2012年第3期|p.745-760|共16页
  • 作者

    Luca Cozzolino; Renata Delia Morte; Giuseppe Del Giudice; Anna Palumbo; Domenico Pianese;

  • 作者单位

    Dipartimento per le Tecnologie, Universita degli Studi di Napoli Parthenope, Centra Direzionale di Napoli, Isola C4, 1-80143 Napoli, Italy;

    Dipartimento per le Tecnologie, Universita degli Studi di Napoli Parthenope, Centra Direzionale di Napoli, Isola C4, 1-80143 Napoli, Italy;

    Dipartimento di Ingegneria Idraulica Geotecnica e Ambientale, universita degli Studi di Napoli Federico If, via Claudio 21,1-80125 Napoli, Italy;

    Dipartimento di Ingegneria Idraulica Geotecnica e Ambientale, universita degli Studi di Napoli Federico If, via Claudio 21,1-80125 Napoli, Italy;

    Dipartimento di Ingegneria Idraulica Geotecnica e Ambientale, universita degli Studi di Napoli Federico If, via Claudio 21,1-80125 Napoli, Italy;

  • 收录信息 美国《科学引文索引》(SCI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    friction; high-order accuracy; shallow-water equations; spectral volume method; well-balancing property; wetting-drying property;

    机译：摩擦;高阶精度浅水方程光谱体积法均衡财产;润湿干燥性;

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