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

• Autor(a) principal: Medeiros, Débora de Oliveira
• Data de Publicação: 2022
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: Biblioteca Digital de Teses e Dissertações da USP
• Texto Completo: https://www.teses.usp.br/teses/disponiveis/55/55134/tde-22082022-133831/
• topic: Derivada generalizada de Lie; Escoamentos viscoelásticos; Finite differences method; Generalized Lie derivative; Método de diferenças finitas; Viscoelastic flows

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.