Analysis of mimetic finite volume schemes on classical and moist shallow water models considering topography based local refinement in spherical Voronoi grids

• Autor(a) principal: Santos, Luan da Fonseca
• Data de Publicação: 2020
• Tipo de documento: Dissertação
• Idioma: eng
• Título da fonte: Biblioteca Digital de Teses e Dissertações da USP
• Texto Completo: https://www.teses.usp.br/teses/disponiveis/45/45132/tde-07052020-154350/
• topic: Equações de água rasa; Finite volume; Geodesic grids; Local refinement; Malhas geodésicas; Malhas não-estruturadas; Moist shallow water model; Non structured grids; Refinamento local; Shallow water equations; Umidade; Volumes finitos

The latitude-longitude grid has been used in global atmospheric models since the early 1960s until today. Nevertheless, the use of this grid creates drawbacks for scalability on massively parallel machines, mainly due to excessive data communication requirements near the poles. Thus, to achieve the required degree of parallelism for the efficient use of massively parallel architectures, the interest in quasi-uniform geodesic grids has increased. Much consideration has been given to icosahedral grids and its pentagonal/hexagonal dual grid. This grid might be optimized using centroidal Voronoi tesselation algorithms that allows us to build local refinements based on a density function. Grids with local refinements have been developed aiming to solve local phenomena without requiring the use of a uniform global grid which can be computationally prohibitive. In this work, aiming to benefit weather forecasting in Brazil, we propose a grid that captures well the Andes mountains and the South American continent. This grid is built through a density function based on topography using centroidal Voronoi tesselation algorithms. The developed density function uses smoothing data techniques on the topography data and has a parameter that allows us to approximately define the ratio between the cell diameters in low and high-resolution regions. The grids developed have a smooth transition between low and high-resolution regions. Using the grids developed, we analyze the use of a mimetic finite volume method for the shallow water equations. Using standard, and more recent shallow-water tests available in the literature, our results show that the refined region generates localized numerical noise in the solution. However, we show how a small amount of diffusion is already enough to mitigate this problem. Additionally, we also implemented a moist shallow water model, where physical precipitation processes are included in the classical shallow-water model. This model is used to investigate the impact of the local refinement on the cloud and rain formation in the South American continent, with results indicating that the refinement greatly affects the model, generating more cloud and rain when compared to the uniform resolution model.