Numerical studies on integro-differential fractional viscoelastic models

• Grant number: 17/21105-6
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: November 01, 2017
• End date: March 31, 2021
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Antonio Castelo Filho
• Grantee: Rosalia Taboada Leiva
• Host 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

Abstract

The modeling of physical phenomena was greatly improved in the recent years, mainly due the continuous development of new mathematical tools (numerical and analytical). Nowadays, numerical simulation of large part of experimental work is a demand, and, the aim is usually the optimization of the process and the reduction of costs. A classical case is the study of fluid flows and solid mechanics, where the numerical modeling plays a major role. For example, it is common to perform a geometry optimization in the formula 1 cars, sailing boats, boards, swimsuits, etc, so that the drag can be reduced, and the structure of the components can be optimized. In these cases, the governing equations are solved using finite element, finite difference, finite volume, spectral, meshless methods, etc, and, due to the complexity of the codes, geometries and meshes involved, most of the times it is practically impossible to prove the converge and stability of the method, and, in some other cases, a true measure of the error is not available. Therefore, these codes rely on the existence of analytical solutions (assuming simple geometries), benchmark problems, and simpler numerical methods (that one can prove the stability, convergence, etc) for validation of their implementation. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

BERTOCO, JULIANA; DE ARAUJO, MANOEL S. B.; LEIVA, ROSALIA T.; SANCHEZ, HUGO A. C.; CASTELO, ANTONIO. Numerical Simulation of KBKZ Integral Constitutive Equations in Hierarchical Grids. APPLIED SCIENCES-BASEL, v. 11, n. 11, JUN 2021. (13/07375-0, 17/21105-6, 20/02990-1)

CASTELO, ANTONIO; AFONSO, ALEXANDRE M.; DE SOUZA BEZERRA, WESLEY. A Hierarchical Grid Solver for Simulation of Flows of Complex Fluids. POLYMERS, v. 13, n. 18, SEP 2021. (20/02990-1, 13/07375-0, 17/21105-6)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

LEIVA, Rosalia Taboada. Numerical Development and Implementation of Generalised Viscoelastic Mo- dels and the Study of Complex Fluids. 2022. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.