Numerical strategies for a miscellany of problems with applications in oil reservoirs and the Navier-Stokes equations

• Grant number: 22/00403-7
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: March 01, 2022
• End date: February 28, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Gilcilene Sanchez de Paulo
• Grantee: Mateus Mitsuo Goto Dakuzaku
• Host Institution: Faculdade de Ciências e Tecnologia (FCT). Universidade Estadual Paulista (UNESP). Campus de Presidente Prudente. Presidente Prudente , SP, Brazil

Abstract

In this project, we intend to solve numerically the Navier-Stokes equations using the finite difference technique and the current-vorticity formulation. To ensure solid knowledge in the area, the student will study numerical methods for prototypes of partial differential equations (PDE) in the light of Navier-Stokes equations, ie, simplified model problems (toy models). The concepts of convergence, stability, consistency, the treatment of boundary conditions, interpretation and presentation of the results, and verification of the accuracy and robustness of the methodologies used will be widely discussed through case studies. The programming language adopted will be Python.(AU)