Numerical study of the natural stress formulation for free surface problems

• Grant number: 16/20389-8
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: January 15, 2017
• End date: July 13, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: José Alberto Cuminato
• Grantee: Irineu Lopes Palhares Junior
• Supervisor: Jonathan David Evans
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: University of Bath, England
• Associated to the scholarship: 14/17348-2 - Stability of Numerical methods for Viscoelastic high Weissenberg number flows, BP.DR

Abstract

In this project, we will investigate a new formulation for solving viscoelastic free surface flows. This methodology is mathematically rooted in a dyadic decomposition of the conformation tensor which results in an efficient method for dealing with stress singularities. The research is focused on benchmark flows in the presence of free surface boundary conditions, e.g. stick-slip and die-swell problems. In the context of a finite difference MAC scheme, it is proposed a study of numerical and asymptotic techniques to deal with the singular points and thus simulate these flows accurately.

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

EVANS, J. D.; PALHARES JUNIOR, I. L.; OISHI, C. M.. Stresses of PTT, Giesekus, and Oldroyd-B fluids in a Newtonian velocity field near the stick-slip singularity. Physics of Fluids, v. 29, n. 12, DEC 2017. (15/50094-7, 14/17348-2, 16/20389-8)

EVANS, J. D.; CUMINATO, J. A.; PALHARES JUNIOR, I. L.; OISHI, C. M.. Numerical study of the stress singularity in stick-slip flow of the Phan-Thien Tanner and Giesekus fluids. Physics of Fluids, v. 31, n. 9, SEP 2019. (13/07375-0, 14/17348-2, 16/20389-8)

EVANS, J. D.; FRANCA, H. L.; PALHARES JUNIOR, I. L.; OISHI, C. M.. Testing viscoelastic numerical schemes using the Oldroyd-B fluid in Newtonian kinematics. Applied Mathematics and Computation, v. 387, p. 32-pg., 2020-12-15. (16/20389-8, 13/07375-0, 14/17348-2, 19/01811-9)