Accuracy and stability analysis of finite-volume methods on unstructured spherical grids for shallow water oceanic models

• Ano de defesa: 2023
• Autor(a) principal: Lapolli, Fabricio Rodrigues
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: FeSOM 2.0; ICON-O; Modelo de água rasa; MPAS-O; NICAM; Numerical instability; Oscilações numéricas; Shallow water model
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/45/45132/tde-19092023-070531/

One important tool at our disposal to evaluate the robustness of Global Circulation Models (GCMs) is to understand the horizontal discretization of the dynamical core under a shallow water approximation and its respective grid. In this thesis, we evaluate the accuracy and stability of different methods used in, or adequate for, unstructured ocean models considering shallow water models. Our work draws a path from the early qualifying dissertation presented in 2021 and the finalized work along with a submitted paper. We evaluated A- (NICAM), B-grid (FeSOM 2.0), and C-grid schemes: one concerning the TRiSK discretization in triangles, the other on hexagons (MPAS) and the ICON horizontal discretization using a modified standard non optimized grid (MODSTD) and a Spherical Circumcentre Voronoi Tessellation (SCVT) grid. Our results show that the schemes have different accuracy capabilities, with the A- (NICAM) and B-grid (FeSOM 2.0) schemes providing at least 1st order accuracy in most operators and time integrated variables, while the C-grid (TRiSK, ICON and MPAS) schemes display more difficulty in adequately approximating the horizontal dynamics depending on the grid use. However, A-grid has shown to be susceptible to the manifestation of computational waves on the MODSTD grid that could contaminate and damage the solution. Moreover, the theory of the inertia-gravity wave representation on regular grids can be extended for our unstructured based schemes, where from least to most accurate we have: A-, B, and C-grid, respectively. Considering only C-grid schemes, TRiSK on triangles most accurately represent the inertia-gravity waves, followed by MPAS and ICON. In terms of stability, we see that the A-grid scheme displays the best stability properties. However, the scheme\'s stability has shown to be influenced by its grid, due to the manifestation of the spurious numerical waves. In contrast, both B-grid and ICON displayed the least stability of all schemes. Finally, in an effort to understand the effects of potential instabilities in ICON, we note that the full 3D model without a filtering term does not destabilize as it is integrated in time. However, the present spurious oscillations are responsible for decreasing the kinetic energy of the oceanic currents. Furthermore, an additional decrease of the currents\' turbulent kinetic energy is also observed, which may play an important role in the weakness of the oceanic currents.