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Computational fluid dynamics of viscoelastic flows

Grant number: 20/02990-1
Support type:Scholarships in Brazil - Post-Doctorate
Effective date (Start): January 01, 2021
Effective date (End): December 31, 2021
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Applied Mathematics
Principal Investigator:Antonio Castelo Filho
Grantee:Hugo Alberto Castillo Sanchez
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


Many of the complex fluids that are of industrial interest (including polymer solutions) exhibit viscoelastic behaviour, i.e. they show both viscous and elastic responses to forces, and thus, their characterisation is particularly important for the industry to estimate the ideal conditions to pump, mix and store them in industrial operations. One of the key features of viscoelastic fluids is the presence of memory; stresses in such fluids depend on the flow history. In addition, these kind of fluids generate stresses that are absent in their Newtonian counterpart, which result in interesting but complex flow phenomena.The modelling and numerical simulation of viscoelastic flows in complex geometries become challenging, especially due to their time-dependent behaviour. For this reason, efficient numerical methods are needed to obtain accurate simulation results. In this project, we are interested in simulate viscoelastic flow problems using a new finite difference method [8] that was recently developed to solve partial differential equations that are derived from Newtonian incompressible flows. This method was compared with other numerical techniques available in the literature and was proven to be an efficient method. In addition, the new finite difference method was extended for the Navier-Stokes equations, showing good convergence results.For the project, we will select a group of different constitutive equations that are able to describe the rheological behaviour of viscoelastic fluids, which will be coupled to the momentum and mass conservation equations, which are described in the following section. These equations will be used to simulate viscoelastic fluids in different flow geometries that are commonly found in industrial processes (such as simple-shear flow, pressure-driven channel flow and sudden-expansion channel).The governing equations (constitutive, continuity and momentum conservation equation) will be solved using the new finite difference method. Once that the accuracy of the method has been tested, our goal will be to develop a computational methodology of viscoelastic flows, which will then be implemented in HIGFLOW software. This software uses finite differences in a staggered grid and its generic in dimensional and type of flow.