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

• Published in: Ocean modelling (Oxford) Vol. 176; p. 102065
• Main Authors: Diamantopoulos, Theodoros, Joshi, Sumedh M., Thomsen, Greg N., Rivera-Rosario, Gustavo, Diamessis, Peter J., Rowe, Kristopher L.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.08.2022
• Subjects: Deflation; Domain decomposition; Non-linear internal waves; Spectral methods; Domain decomposition; Deflation; Non-linear internal waves; Spectral methods
• ISSN: 1463-5003; 1463-5011
• DOI: 10.1016/j.ocemod.2022.102065

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. •A hybrid high-order non-hydrostatic stratified flow solver is presented.•Spatial discretization accounts for long complex computational domains.•Preconditioning of the pressure Poisson equation for such domains is addressed.•Unstratified and stratified benchmarks are performed.•Three-dimensional shoaling of a breaking internal solitary wave is simulated.