A vertically-Lagrangian, non-hydrostatic, multilayer model for multiscale free-surface flows
A vertically-Lagrangian, non-hydrostatic, multilayer model for multiscale free-surface flows
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用于多尺度自由表面流的垂直拉格朗日非静水多层模型
DOI：
10.1016/j.jcp.2020.109609
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
S. Popinet
中科院分区：
文献类型：
--
作者：
S. Popinet
本文提出了一个半离散的，多层的方程组，描述了三维运动的不可压缩流体的地形和移动的自由表面上的限制下。该系统是不可压缩欧拉方程的一致离散化，在没有对界面斜率进行假设的情况下有效。表达为一组守恒定律的每一层，制定了一个明确的物理解释，并使流体静力学圣维南方程，分散Boussinesq风格的模型和不可压缩的欧拉方程之间的无缝连接。基于近似垂直投影和多重网格加速柱松弛的相关数值方案为所有状态提供了准确且有效的解决方案。因此，相同的模型可以应用于研究米级的波浪，甚至超过打破，与使用小尺度欧拉/纳维-斯托克斯模型获得的结果密切匹配，以及沿海或全球尺度的色散波，精度和效率与扩展Boussinesq波模型相当。作为Basilisk框架的一部分，该实施是自适应的，并行的和开源的，并且提供了足以重现所有结果和图形的源代码。
This article presents a semi-discrete, multilayer set of equations describing the three-dimensional motion of an incompressible fluid bounded below by topography and above by a moving free-surface. This system is a consistent discretisation of the incompressible Euler equations, valid without assumptions on the slopes of the interfaces. Expressed as a set of conservation laws for each layer, the formulation has a clear physical interpretation and makes a seamless link between the hydrostatic Saint-Venant equations, dispersive Boussinesq-style models and the incompressible Euler equations. The associated numerical scheme, based on an approximate vertical projection and multigrid-accelerated column relaxations, provides accurate and efficient solutions for all regimes. The same model can thus be applied to study metre-scale waves, even beyond breaking, with results closely matching those obtained using small-scale Euler/Navier–Stokes models, and coastal or global scale dispersive waves, with an accuracy and efficiency comparable to extended Boussinesq wave models. The implementation is adaptive, parallel and open source as part of the Basilisk framework and the documented source codes sufficient to reproduce all results and figures are provided.