Numerical approximation of interface curvature: volume fractions and application of neural network

• Grant number: 20/05963-5
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Effective date (Start): August 01, 2020
• Effective date (End): August 31, 2021
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Cassio Machiaveli Oishi
• Grantee: Diego Alecsander de Aguiar
• Host Institution: Faculdade de Ciências e Tecnologia (FCT). Universidade Estadual Paulista (UNESP). Campus de Presidente Prudente. Presidente Prudente , SP, Brazil
• Associated research grant: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry, AP.CEPID

Abstract

In this project, we will investigate the numerical computation of interface curvature. The interface will be described in the context of implicit representation framework, particularly focusing on the construction via volume fractions of the Volume-of-Fluid (VoF). Initially, the student will be introduced to the basic concepts of the VoF, as for instance the idea concerning the volume fractions and the geometrical representation of the interface on structured meshes. After, it will be studied the definition of curvature, including its formal definition by differential geometry, and the approximation via volume fractions. Finally, the student will investigate the ideas for application of neural network combined with the volume fractions concept in order to estimate the curvature of different interfaces.