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.
News published in Agência FAPESP Newsletter about the scholarship: