Numerical methods for the coupled Shallow-Water-Exner system

• Grant number: 24/06306-9
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: June 01, 2024
• End date: May 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Maicon Ribeiro Correa
• Grantee: Thiago Felipe Castro Carrenho
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry, AP.CEPID

Abstract

This Research project in Numerical Analysis is oriented to the study of the Shallow Waters equations, particularly its one-dimensional version, also known as the Saint-Venant equations, and the Exner equation, which consists of a system of balance laws of hyperbolic nature. From a numerical point of view, we propose a computational implementation and the application of high-order central finite volume schemes for hyperbolic balance laws and Discontinuous Galerkin type finite element schemes, allowing the numerical resolution of the Shallow-Waters-Exner system, with subsequent simulation of problems of flows in natural channels with transport of sediments eroded from the bed.