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

Diamantopoulos, Theodoros; Joshi, Sumedh; Thomsen, Greg; Rivera-Rosario, Gustavo; Diamessis, Peter; Rowe, Kristopher

doi:10.1016/j.ocemod.2022.102065

Title: 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

Journal Article · Mon Aug 01 00:00:00 EDT 2022 · Ocean Modelling

DOI:https://doi.org/10.1016/j.ocemod.2022.102065· OSTI ID:1889461

Diamantopoulos, Theodoros; Joshi, Sumedh; Thomsen, Greg; Rivera-Rosario, Gustavo; Diamessis, Peter; Rowe, Kristopher

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.

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Research Organization:: Argonne National Lab. (ANL), Argonne, IL (United States)

Sponsoring Organization:: National Science Foundation (NSF)

DOE Contract Number:: AC02-06CH11357

OSTI ID:: 1889461

Journal Information:: Ocean Modelling, Vol. 176

Country of Publication:: United States

Language:: English

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