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Numerical simulation of free surface complex flows

Grant number: 19/01811-9
Support Opportunities:Scholarships in Brazil - Doctorate
Effective date (Start): March 01, 2019
Effective date (End): June 30, 2023
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Applied Mathematics
Principal Investigator:José Alberto Cuminato
Grantee:Hugo Leonardo França
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):21/14953-6 - Numerical studies of capillary effects on non-Newtonian droplet dynamics, BE.EP.DR


In this doctoral project it is proposed the development of an axisymmetric code for the solution of complex fluid flows, i.e. materials combining viscosity, elasticity and plasticity effects. The applications of interest are flows with free surfaces and with topological changes, as in the case of the impact of droplets in different types of surface (rigid or fluid layer) and the coalescence of non-Newtonian droplets. In order to solve problems of industrial interest, besides the study of rheological properties, the effect of surface tension in the mathematical modeling will also be considered, this adds complexities in simulating flows involving the impact of drops. The mathematical model adopted will involve equations which describe incompressible flows with free surfaces coupled to constitutive equation sthat describe an elastoviscoplastic material. In addition, there should be considered the equations that describe the thixotropic behavior of the material and also the energy equation to capture non-isothermal effects on the flow. From the computational point of view, the method adopted for the treatment and dynamics of the free surface will be front-tracking combined with the MAC Method (Marker-And-Cell). (AU)

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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)
FRANCA, HUGO L.; OISHI, CASSIO M.; THOMPSON, RONEY L.. Numerical investigation of shear-thinning and viscoelastic binary droplet collision. Journal of Non-Newtonian Fluid Mechanics, v. 302, p. 15-pg., . (13/07375-0, 19/01811-9)
FRANCA, HUGO L.; OISHI, CASSIO M.. A machine learning strategy for computing interface curvature in Front-Tracking methods. Journal of Computational Physics, v. 450, p. 9-pg., . (13/07375-0, 19/01811-9)
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., . (16/20389-8, 18/22242-0, 13/07375-0, 14/17348-2, 19/01811-9)
Academic Publications
(References retrieved automatically from State of São Paulo Research Institutions)
FRANÇA, Hugo Leonardo. Numerical simulation of complex fluid flows with moving interfaces. 2023. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.

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