Numerical Methods for Non-Newtonian Free Surface Flows: effects of surface tension

• Grant number: 17/11428-2
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: August 01, 2017
• End date: November 30, 2021
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: José Alberto Cuminato
• Grantee: Débora de Oliveira Medeiros
• 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): 19/08742-2 - Stabilization schemes for solving viscoelastic free surface flows with surface tension effects, BE.EP.DR

Abstract

This project proposes the study of numerical methods for the solution of incompressible and non-Newtonian fluid flows, with emphasis on the effects of surface tension. Mathematical modeling involves the Navier-Stokes equations and a system of equations that define the contribution of the non-Newtonian tensor. In addition, the modeling will use the conditions of free surface contour considering the incorporation of the surface tension. In the context of the MAC method, the numerical formulation will combine a discretization of finite differences with a projection method and a representation of the interface (free surface) by the method of marking (Front-tracking). The numerical methods developed will be applied to the solution of micro-flows of complex fluids. In this class of problems, in addition to the difficulties encountered in the treatment of the equations that define the non-Newtonian model, a challenge is the accurate numerical treatment of the effects of surface tension. Therefore, this doctoral project aims to expand the use of computational tools for the solution of industrial problems and applications of science and engineering.

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)

REDDY, GUJJI MURALI MOHAN; SEITENFUSS, ALAN B.; MEDEIROS, DEBORA DE OLIVEIRA; MEACCI, LUCA; ASSUNCAO, MILTON; VYNNYCKY, MICHAEL. A Compact FEM Implementation for Parabolic Integro-Differential Equations in 2D. ALGORITHMS, v. 13, n. 10, OCT 2020. (16/19648-9, 18/07643-8, 17/11428-2)

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)

Academic Publications

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

MEDEIROS, Débora de Oliveira. Numerical analysis of finite difference schemes for constitutive equations in viscoelastic fluid flows. 2022. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.