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A numerical method for the treatment of topological changes in viscoelastic free surface flows

Grant number: 16/00456-2
Support type:Scholarships in Brazil - Master
Effective date (Start): April 01, 2016
Effective date (End): September 29, 2018
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Applied Mathematics
Principal Investigator:Cassio Machiaveli Oishi
Grantee:Hugo Leonardo França
Home 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
Associated scholarship(s):17/04471-9 - Numerical solution of viscoelastic free surface problems with complex topological changes, BE.EP.MS


This work presents the study of a numerical method for solving the incompressible Navier-Stokes equations for free-surface flows that undergo topological changes. The governing equations are solved through a projection method that decouples the velocity and pressure fields. The discretization is performed via finite differences approximations applied to a non-uniform mesh. The numerical scheme is applied for solving Newtonian and non-Newtonian fluid flows. In particular, the viscoelastic effects are described by the Oldroyd-B model, using the classic Cartesian formulation and also an alternative approach for the decomposition of the polimeric part of the extra stress tensor. This alternative decomposition strategy is known as Natural Stress Formulation, and numerical results are originally discussed in this work. The new code with a non-uniform mesh is tested in the following problems: the lid-driven cavity, the cross-slot problem, and the flow through a channel with contraction. In order to represent the free-surface, a Front-Tracking method that describes the interface explicitly using marker particles is used. The algorithm for topological changes is based in a technique that detects when the interface is tangled and untangles it. This algorithm is tested in numerical simulations such as: the impact between a drop and a layer of fluid, the impact between drops and a solid wall, and the jetting break-up process under the effect of surface tension.

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, JONATHAN D.; FRANCA, HUGO L.; OISHI, CASSIO M. Application of the natural stress formulation for solving unsteady viscoelastic contraction flows. Journal of Computational Physics, v. 388, p. 462-489, JUL 1 2019. Web of Science Citations: 2.
Academic Publications
(References retrieved automatically from State of São Paulo Research Institutions)
FRANÇA, Hugo Leonardo. Um método numérico para o tratamento de mudanças topológicas em escoamentos viscoelásticos com superfície livre. 2018. Master's Dissertation - Universidade Estadual Paulista "Júlio de Mesquita Filho" Faculdade de Ciências e Tecnologia..

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