Analysis of finite volume schemes for spherical geodesic grids with local refinement

• Grant number: 17/25191-4
• Support Opportunities: Scholarships in Brazil - Master
• Start date: March 01, 2018
• End date: February 29, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Pedro da Silva Peixoto
• Grantee: Luan da Fonseca Santos
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 16/18445-7 - Numerical methods for the next generation weather and climate models, AP.JP

Abstract

Numerical models for atmospheric dynamics, a central piece in weather and climate forecasting, are going through radical changes in order to become adequate for the next generation supercomputers that demand massively parallel processing. Quasi-uniform spherical grids avoids scalability problems encountered in traditional models, but creates challenges for the development of numerical schemes. Several modern models adopt finite volume schemes that ensure certain desirable properties. These numerical approaches have been studied for quasi-uniform grids, and these are highly susceptible to grid interference. However, these grids are flexible and allow local refinements with smooth transitions. This project aims to study numerical methods for the shallow water equations on quasi uniform grids, focusing on locally refined grids. Specifically, we wish to study the benefits and problems involved in the use of locally refined grid over the Andes, which have an important role on the climate of Southeast region of Brazil. This local refinement may bring great benefit to weather forecasting and regional climate modelling, however, the numerical effects of using such refined grids have not yet been fully understood, and this is the gap this project aims to fill. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

SANTOS, LUAN F.; PEIXOTO, PEDRO S.. Topography-based local spherical Voronoi grid refinement on classical and moist shallow-water finite-volume models. Geoscientific Model Development, v. 14, n. 11, p. 6919-6944, NOV 16 2021. (16/18445-7, 17/25191-4)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

SANTOS, Luan da Fonseca. Analysis of mimetic finite volume schemes on classical and moist shallow water models considering topography based local refinement in spherical Voronoi grids. 2020. Master's Dissertation - Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) São Paulo.