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Numerical simulation of free surface complex flows

Grant number: 19/01811-9
Support type:Scholarships in Brazil - Doctorate
Effective date (Start): March 01, 2019
Effective date (End): February 28, 2021
Field of knowledge:Physical Sciences and Mathematics - Mathematics
Principal Investigator:José Alberto Cuminato
Grantee:Hugo Leonardo França
Home 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


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)