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首页> 外文期刊>Ocean Engineering >A higher-order σ-coordinate non-hydrostatic model for nonlinear surface waves
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A higher-order σ-coordinate non-hydrostatic model for nonlinear surface waves

机译：非线性表面波的高阶σ坐标非静水模型

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摘要

A higher-order non-hydrostatic model in a σ-coordinate system is developed. The model uses an implicit finite difference scheme on a staggered grid to simultaneously solve the unsteady Navier-Stokes equations (NSE) with the free-surface boundary conditions. An integral method is applied to resolve the top-layer non-hydrostatic pressure, allowing for accurately resolving free-surface wave propagation. In contrast to the previous work, a higher-order spatial discretization is utilized to approximate the large horizontal pressure gradient due to steep surface waves or rapidly varying topographies. An efficient direct solver is developed to solve the resulting block hepta-diagonal matrix system. Accuracy of the new model is validated by linear and nonlinear standing waves and progressive waves. The model is then used to examine freak (extreme) waves. Features of downshifting focusing location and wave asymmetry characteristics are predicted on the temporal and spatial domains of a freak wave.
机译：建立了σ坐标系中的高阶非静水模型。该模型在交错网格上使用隐式有限差分方案，同时用自由表面边界条件求解非定常的Navier-Stokes方程（NSE）。应用积分方法来解决顶层非静水压力，从而可以精确解决自由表面波的传播。与先前的工作相反，由于表面波陡峭或地形变化迅速，利用高阶空间离散化来近似较大的水平压力梯度。开发了一种有效的直接求解器来求解所得的块七角形对角矩阵系统。新模型的准确性通过线性和非线性驻波以及渐进波来验证。然后将模型用于检查异常（极端）波。在怪胎波的时空域上预测了降档聚焦位置的特征和波的不对称特性。

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