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An unstructured finite volume numerical scheme for extended 2D Boussinesq-type equations

机译：扩展二维Boussinesq型方程的非结构化有限体积数值格式

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摘要

We present a high-order well-balanced unstructured finite volume (FV) scheme on triangular meshes for modeling weakly nonlinear and weakly dispersive water waves over slowly varying bathymetries, as described by the 2D depth-integrated extended Boussinesq equations of Nwogu, rewritten here in conservation law form. The FV scheme numerically solves the conservative form of the equations following the median dual node-centered approach, for both the advective and dispersive part of the equations. For the advective fluxes, the scheme utilizes an approximate Riemann solver along with a well-balanced topography source term upwinding. Higher order accuracy in space and time is achieved through a MUSCL-type reconstruction technique and through a strong stability preserving explicit Runge-Kutta time stepping. Special attention is given to the accurate numerical treatment of moving wet/dry fronts and boundary conditions. The model is applied to several examples of non-breaking wave propagation over variable topographies and the computed solutions are compared to experimental data. The presented results indicate that the presented FV model is robust and capable of simulating wave transformations from relatively deep to shallow water, providing accurate predictions of the wave's propagation, shoaling and runup.
机译：我们在三角网格上提出了一种高阶均衡的非结构有限体积（FV）方案，用于在缓慢变化的水深上模拟弱非线性和弱弥散水波，如Nwogu的二维深度积分扩展Boussinesq方程所描述，在此处重写守法形式。对于方程组的对流和分散部分，FV方案按照中值双节点中心法在数值上求解方程组的保守形式。对于平流，该方案利用了近似的黎曼求解器以及良好平衡的地形源上风。通过MUSCL类型的重构技术以及强大的稳定性，可以保留显式的Runge-Kutta时间步长，从而实现了更高的时空精度。特别注意移动的湿/干前沿和边界条件的精确数值处理。该模型被应用于可变地形上非破坏波传播的几个示例，并将计算出的解与实验数据进行了比较。给出的结果表明，所提出的FV模型是健壮的，能够模拟从相对深水到浅水的波浪转换，从而提供了对波浪传播，浅滩和径流的准确预测。

著录项

  • 来源
    《Coastal engineering》 |2012年第2012期|p.42-66|共25页
  • 作者

    M. Kazolea; A.I. Delis; I.K. Nikolos; C.E. Synolakis;

  • 作者单位

    Environmental Engineering Department, Technical University of Crete, University Campus, Chania, Crete 73100, Greece;

    Department of Sciences, Division of Mathematics, Technical University of Crete, University Campus, Chania, Crete, Greece;

    Department of Production Engineering & Management, Technical University of Crete, University Campus, Chania, Crete 73100, Greece;

    Environmental Engineering Department, Technical University of Crete, University Campus, Chania, Crete 73100, Greece;

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

    boussinesq-type equations; finite volumes; unstructured meshes; well-balancing; solitary waves; regular waves; runup;

    机译：boussinesq型方程;有限的体积非结构化网格;均衡;孤波定期波浪启动;

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