In this project we propose the analysis and implementation of numerical methods for the solution of incompressible viscoelastic fluids flows that exhibit transient behavior . In this study the aim is to analyze the stability of numerical methods , proposing efficient and accurate techniques for the solution of the constitutive equations that model the viscoelastic behavior , with special attention to the stability of these methods when applied to problems with high Weissenberg number ( Wi $ $ ) . The number Wi $ $ is the ratio between the relaxation time of the viscoelastic fluid and the inertial flow time. From the standpoint of applications, the appearance of instabilities will be investigated (physical) induced by non -Newtonian fluids in different geometry when the Weissenberg number is high, involving or not free surface boundary conditions (mobile interfaces). Therefore, combining these new numerical techniques, it is possible to investigate important and difficult practical problems that would have been impossible to simulate by traditional methods, and provide the research group with robust tools capable of simulating more complex scientific and technological problems of interest in practical applications.
News published in Agência FAPESP Newsletter about the scholarship: