Numerical treatment of the normal stress boundary condition for projection methods in free surface flows

• Grant number: 15/01243-0
• Support Opportunities: Scholarships in Brazil - Master
• Start date: May 01, 2015
• End date: February 28, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Cassio Machiaveli Oishi
• Grantee: Débora de Oliveira Medeiros
• 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 treatment of the normal stress condition for projection methods in free surface flows. This condition, which is used to impose the pressure at the free surface, will be discretized by an implicit strategy in order to enhance the numerical stability of the projection method for solving the Navier-Stokes equations. In particular, we will study the construction of a formulation that involves the solution of a superficial laplacian in combination with the Poisson equation of the projection method. In the context of the MAC and front-tracking formulations, in order to apply an accurate solution of the superficial laplacian, numerical computations of the free-surface curvature will be also investigated. Finally, the numerical method will be tested using reference solutions and applied in moving free surface flows. (AU)