A high accuracy/resolution spectral element/Fourier–Galerkin method for the simulation of shoaling non-linear internal waves and turbulence in long domains with variable bathymetry
A high accuracy/resolution spectral element/Fourier–Galerkin method for the simulation of shoaling non-linear internal waves and turbulence in long domains with variable bathymetry
复制标题
一种高精度/分辨率谱元/傅里叶伽辽金方法，用于模拟可变测深长域中的浅滩非线性内波和湍流
DOI：
10.1016/j.ocemod.2022.102065
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发表时间：
2022
期刊：
影响因子：
3.2
通讯作者：
Rowe, Kristopher L.
中科院分区：
文献类型：
--
作者：
Diamantopoulos, Theodoros;Joshi, Sumedh M.;Thomsen, Greg N.;Rivera-Rosario, Gustavo;Diamessis, Peter J.;Rowe, Kristopher L.
本文提出了一种高阶混合连续-Galerkin数值方法，用于模拟长计算区域内复杂水深条件下的非线性、非静力内波和湍流。在非周期波传播方向上的空间离散，利用节点谱元法。这种基于高阶元素的离散化允许高度精确地表示复杂的域几何形状沿着将分辨率集中在感兴趣区域的灵活性。在非线性内波的法线到等深线传播的假设下，通过傅立叶-伽辽金离散化将第三周期方向并入。非线性内波的独特的非流体静力性质，以及其中的任何不稳定性和湍流，需要压力泊松问题的数值求解。这项工作的一个定义功能是应用程序的区域分解方法，结合块雅可比/放气为基础的预处理的压力泊松问题。这种组合方法特别适合于感兴趣的长的高纵横比的复杂域，并且能够有效地高精度再现非线性内波的非流体静力学动力学。实施细节也描述了求解器的稳定性及其并行化策略的上下文中。一系列日益复杂的基准测试证明了流量求解器的鲁棒性。基准最终与三维模拟的对流打破模式一个非线性内波在一个现实的中国南海测深断面和背景流/层化剖面。
A high-order hybrid continuous-Galerkin numerical method, designed for the simulation of non-linear, non-hydrostatic internal waves and turbulence in long computational domains with complex bathymetry, is presented. The spatial discretization in the non-periodic wave-propagating directions, utilizes the nodal spectral element method. Such a high-order element-based discretization allows the highly accurate representation of complex domain geometry along with the flexibility of concentrating resolution in areas of interest. Under the assumption of the normal-to-isobath propagation of non-linear internal waves, a third periodic direction is incorporated via a Fourier–Galerkin discretization. The distinct non-hydrostatic nature of non-linear internal waves and, any instabilities and turbulence therein, necessitates the numerically challenging solution of the pressure Poisson problem. A defining feature of this work is the application of a domain decomposition approach, combined with block-Jacobi/deflation-based preconditioning to the pressure Poisson problem. Such a combined approach is particularly suitable for the long high aspect-ratio complex domains of interest and enables the efficient high-accuracy reproduction of the non-hydrostatic dynamics of non-linear internal waves. Implementation details are also described in the context of the stability of the solver and its parallelization strategy. A series of benchmarks of increasing complexity demonstrate the robustness of the flow solver. The benchmarks culminate with the three-dimensional simulation of a convectively breaking mode-one non-linear internal wave over a realistic South-China-Sea bathymetric transect and background current/stratification profiles.