Stabilization schemes for solving viscoelastic free surface flows with surface tension effects

• Grant number: 19/08742-2
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: July 01, 2019
• End date: June 30, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: José Alberto Cuminato
• Grantee: Débora de Oliveira Medeiros
• Supervisor: Hirofumi Notsu
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: Kanazawa University, Japan
• Associated to the scholarship: 17/11428-2 - Numerical Methods for Non-Newtonian Free Surface Flows: effects of surface tension, BP.DR

Abstract

In this project, we propose to investigate some recent methodologies to treat high elasticity fluid flows. In particular, we are interested dealing with viscoelastic free surface flows considering the effects of surface tension, as for example, the die-swell extrusion and injection moulding problems. The constitutive equations used to model the rheological behavior of the fluids will be reformulated based on energy estimate analysis. Moreover, we suggest study and include a Lagrangian framework to solve the equations studying the characteristic in order to enhance the stability of the numerical schemes. Finally, these techniques will be extended for solving free surface problems using a finite difference discretization combined with MAC and front-tracking schemes. (AU)

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)

MEDEIROS, DEBORA D.; NOTSU, HIROFUMI; OISHI, CASSIO M.. SECOND-ORDER FINITE DIFFERENCE APPROXIMATIONS OF THE UPPER-CONVECTED TIME DERIVATIVEtextbackslash{}ast. SIAM JOURNAL ON NUMERICAL ANALYSIS, v. 59, n. 6, p. 2955-2988, 2021. (13/07375-0, 17/11428-2, 19/08742-2)