Analysis and development of finite volume methods for the new generation of cubed sphere dynamical cores for the atmosphere

• Grant number: 20/10280-4
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: December 01, 2020
• End date: March 31, 2024
• 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

The global atmospheric model FV3 from GFDL-NOAA-USA, which was originally designed for latitude-longitude grids, was adapted to the cubed sphere aiming to improve its scalability in massively parallel supercomputers. However, in this kind of grid, we are more likely to have grid imprinting problems. Besides that, the FV3 model lacks some highly desirable mimetic properties. This work aims to analyze the properties of the finite volume discretizations employed in the global atmospheric model FV3 on the cubed-sphere. We will investigate how the properties of the cells may impact on the accuracy of the numerical schemes. This study will firstly implement a cubed-sphere grid generator and the FV3 discrete operators on this grid. Then, we will and analyze how the cubed-sphere grid properties influence in the numerical schemes by assessing it using the classical shallow-water model and a convective shallow water model. We will study the numerical dispersion and conservations properties of the scheme aiming to propose modifications in the numerical schemes to develop a mimetic finite volume version of the model. Then, we shall develop a local refinement on the cubed-sphere and investigate how it impacts the numerical solution. As a final stage of the 3D development, we will analyze and include the Lagrangian vertical discretization of the FV3 model and investigate how the horizontal discretization aspects can impact on the full three-dimensional model. (AU)

Academic Publications

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

SANTOS, Luan da Fonseca. Analysis of finite-volume advection schemes on cubed-sphere grids and an accurate alternative for divergent winds. 2024. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) São Paulo.