Abstract The unstructured mesh, discontinuous Galerkin finite element discretisation based coastal ocean model, Thetis, has been extended to include non-hydrostatic (buoyancy-driven and free surface) dynamics. Two alternative approaches to achieve this are described in this work. The first (a 3D based algorithm) makes use of prismatic element based meshes and uses a split-step pressure projection method for baroclinic and barotropic modes, while the second (a 2D based algorithm) adopts a novel multi-layer approach to convert a 3D problem into a combination of multiple 2D computations with only 2D triangle meshes required. Model development is carried out at high-level with the Firedrake library, using code generation techniques to automatically produce low-level code for the discretised model equations in an efficient and rapid manner. Through comparisons against several barotropic/baroclinic test cases where non-hydrostatic effects are important, the implemented approaches are verified and validated, and the proposed algorithms compared. Depending on whether the problems are dominated by dispersive, baroclinic or barotropic features, recommendation are given over the use of full 3D or multi-layer 2D based approaches to achieve optimal computational accuracy and efficiency. It is demonstrated that while in general the 2D approach is well-suited for barotropic problems and dispersive free surface waves, the 3D approach is more advantageous for simulating baroclinic buoyancy-driven flows due in part to the high vertical resolution typically required to represent the active tracer fields.

中文翻译：

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非流体静力扩展与非连续有限元沿海海洋模型的比较

摘要 基于非结构化网格、不连续 Galerkin 有限元离散化的沿海海洋模型 Thetis 已扩展到包括非流体静力（浮力驱动和自由表面）动力学。在这项工作中描述了实现这一目标的两种替代方法。第一种（基于 3D 的算法）利用基于棱柱单元的网格，并对斜压和正压模式使用分步压力投影方法，而第二种（基于 2D 的算法）采用新颖的多层方法来转换 3D将问题转化为多个 2D 计算的组合，只需要 2D 三角形网格。模型开发是通过 Firedrake 库在高层进行的，使用代码生成技术以高效快速的方式为离散模型方程自动生成低层代码。通过与几个非流体静力效应很重要的正压/斜压测试案例的比较，验证和验证了所实现的方法，并比较了所提出的算法。根据问题是由色散、斜压还是正压特征主导，建议使用基于全 3D 或多层 2D 的方法来实现最佳计算精度和效率。结果表明，虽然通常 2D 方法非常适合正压问题和色散自由表面波，但 3D 方法更适合模拟斜压浮力驱动的流动，部分原因是通常需要高垂直分辨率来表示活动示踪字段。