Local refinement and interpolation in spherical icosahedral grids

• Grant number: 17/11542-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: July 01, 2017
• End date: December 31, 2017
• 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

Some physics problems like weather prediction and ocean modelling adopt the sphere as basic domain. These problems require the numerical solution of the differential equations that model the fluid dynamics. Therefore, discretizations of the sphere are necessary to numerically solve the equations. In meteorological models, the most common discretization of the sphere, used since 1960's until today (Staniforth and Thuburn (2011)), is the latitude-longitude grid. Nevertheless, this has been changing due to the increased degree of parallelism required for efficient use of modern supercomputers. The interest in novel quasi-uniform spherical grids, mainly the icosahedral based, has greatly increased, as it is viewed as a way to make better use of parallel computing resources. Therefore, in this project we propose to study icosahedral spherical grids. We will study locally refined icosahedral grids and, in particular, we intend to build grids that would be able to capture well the Andes' region. The icosahedral grids we will study will be optimized using Centroidal Voronoi Tessellation algorithms (Ju et al. (2011)). We will also study ways to interpolate to and from icosahedral grids, as it is required in dynamical atmospheric modelling (Peixoto (2013)). To generate the icosahedral grids we will use the iModel software pack, developed by (Peixoto (2013)). The computing language adopted is Fortran. We will use the computers of the Applied Mathematics Laboratory of the IME-USP. (AU)