Numerical analysis of finite difference schemes for constitutive equations in viscoelastic fluid flows

Author(s)

Débora de Oliveira Medeiros

• Document type: Doctoral Thesis
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2022-06-20

Examining board members

José Alberto Cuminato; Daniel Onofre de Almeida Cruz; Taygoara Felamingo de Oliveira; Leandro Franco de Souza

• Advisor: José Alberto Cuminato; Cássio Machiaveli Oishi

Abstract

In this work, we present a study of numerical methods for the solution of incompressible fluid flows, with emphasis on viscoelastic effects. The upper-convected derivative term is rewritten, using the definition of the generalized Lie derivative in a Lagrangian framework, providing a new numerical scheme for viscoelastic fluid flows. The mathematical modeling involves the Navier-Stokes equations and a system of equations that define the contribution of the polymer stress tensor. The numerical formulation combines a finite difference discretization, in the MAC context, with a projection method and the reformulation of the constitutive equation. We carried out theoretical analyses of the proposed methods, convergence studies of simple problems, and applications to the solution of complex fluid flows. The numerical results agree with the theory developed, present results fairly comparable with other numerical methods from the literature, and allowing a discussion about the numerical instabilities of high Weissenberg number problems. (AU)

• FAPESP's process: 17/11428-2 - Numerical Methods for Non-Newtonian Free Surface Flows: effects of surface tension
• Grantee: Débora de Oliveira Medeiros
• Support Opportunities: Scholarships in Brazil - Doctorate