Numerical Development and Implementation of Generalised Viscoelastic Mo- dels and the Study of Complex Fluids

Author(s)

Rosalía Taboada Leiva

• Document type: Doctoral Thesis
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2022-08-11

Examining board members

Antonio Castelo Filho; Célio Bruno Pinto Fernandes; Oscar Mauricio Hernandez Rodriguez; Leandro Franco de Souza

• Advisor: Antonio Castelo Filho; Luis Jorge Lima Ferras

Abstract

The modeling of physical phenomena has greatly improved in recent years, mainly thanks to the continuous development of new mathematical tools (numerical and analytical). Today, numerical simulation of much of the experimental work is in demand, and the goal is usually process optimization and cost reduction. A classical case is the study of fluid flow and solid mechanics, where numerical modeling plays a key role. In recent decades, much attention has been paid to fractional modeling, where the typical integer order derivative is replaced by a non-integer one, leading to a more general definition of the derivative and a more general definition of (systems of) differential equations. In this work, we are interested in the numerical solution of constitutive modeling equations using functions resulting from fractional calculus to model viscoelastic materials. Therefore, in this work, we start by showing the connection between the classical and fractional Maxwell viscoelastic models and present the basic theory behind these constitutive equations. We then develop new generalized models that provide good modeling of various viscoelastic materials, but do not exhibit the problems with singular kernels that occur in fractional models (singular kernels pose a problem in the numerical implementation of the models). The new models will be implemented in general numerical codes, in particular the HiG-Flow code. The numerical implementation will be verified by developing new analytical solutions and comparing more complex numerical solutions with reference results from the literature. (AU)

• FAPESP's process: 17/21105-6 - Numerical studies on integro-differential fractional viscoelastic models
• Grantee: Rosalia Taboada Leiva
• Support Opportunities: Scholarships in Brazil - Doctorate