Abstract This paper aims to present the extension of the non-hydrostatic wave-flow model SWASH with the covolume method to build discretization schemes on unstructured triangular grids. Central to this method that is free of spurious pressure modes, is the use of dual pairs of meshes that are mutually orthogonal, such as the Delaunay-Voronoi mesh systems. The approximants sought are the components of the flow velocity vector normal to the cell faces of the primal mesh. In addition to the covolume approach, a novel upwind difference scheme for the horizontal advection terms in the momentum equation is proposed. This scheme obeys the Rankine-Hugoniot jump relations and prevents the odd-even decoupling of the velocity field accordingly. Moreover, cases with flow discontinuities, such as steady bores and broken waves, are properly treated. In spite of the low-order accuracy of the proposed method, unstructured meshes easily allow for local refinement in a way that retains the desired accuracy. The unstructured-grid version of SWASH is applicable to a wide range of 2DH wave-flow problems to investigate the nonlinear dynamics of free surface waves over varying bathymetries. Its efficiency and robustness is tested on a number of these problems employing unstructured triangular meshes.

中文翻译：

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在非结构化网格上用 SWASH 计算沿海水域的自由表面波

摘要 本文旨在介绍非静水波流模型SWASH 与covolume 方法的扩展，以在非结构化三角形网格上建立离散化方案。这种没有虚假压力模式的方法的核心是使用相互正交的双网格对，例如 Delaunay-Voronoi 网格系统。寻求的近似值是垂直于原始网格单元面的流速矢量的分量。除了covolume方法之外，还提出了动量方程中水平对流项的一种新的迎风差分格式。该方案遵循Rankine-Hugoniot跳跃关系，并相应地防止速度场的奇偶解耦。此外，适当处理具有流动不连续性的情况，例如稳定孔和断波。尽管所提出的方法的精度较低，但非结构化网格很容易以保持所需精度的方式进行局部细化。SWASH 的非结构化网格版本适用于范围广泛的 2DH 波流问题，以研究不同水深范围内自由表面波的非线性动力学。它的效率和鲁棒性在许多使用非结构三角形网格的问题上进行了测试。