Stability of Numerical methods for Viscoelastic high Weissenberg number flows

• Grant number: 14/17348-2
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: September 01, 2014
• End date: December 01, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: José Alberto Cuminato
• Grantee: Irineu Lopes Palhares Junior
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry, AP.CEPID
• Associated scholarship(s): 16/20389-8 - Numerical study of the natural stress formulation for free surface problems, BE.EP.DR

Abstract

In this project we propose the analysis and implementation of numerical methods for the solution of incompressible viscoelastic fluids flows that exhibit transient behavior . In this study the aim is to analyze the stability of numerical methods , proposing efficient and accurate techniques for the solution of the constitutive equations that model the viscoelastic behavior , with special attention to the stability of these methods when applied to problems with high Weissenberg number ( Wi $ $ ) . The number Wi $ $ is the ratio between the relaxation time of the viscoelastic fluid and the inertial flow time. From the standpoint of applications, the appearance of instabilities will be investigated (physical) induced by non -Newtonian fluids in different geometry when the Weissenberg number is high, involving or not free surface boundary conditions (mobile interfaces). Therefore, combining these new numerical techniques, it is possible to investigate important and difficult practical problems that would have been impossible to simulate by traditional methods, and provide the research group with robust tools capable of simulating more complex scientific and technological problems of interest in practical applications.

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)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

PALHARES JUNIOR, Irineu Lopes. Numerical analysis of viscoelastic flows with singularities. 2019. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.