SECOND-ORDER FINITE DIFFERENCE APPROXIMATIONS OF THE UPPER-CONVECTED TIME DERIVATIVEtextbackslash{}ast

Autor(es)

Medeiros, Debora D. ^[1] ; Notsu, Hirofumi ^[2] ; Oishi, Cassio M. ^[3]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Dept Matemat Aplicada & Estat, Inst Ciencias Matemat & Comp ICMC, Campus Sao Carlos, BR-1025480 Sao Paulo, SP - Brazil

^[2] Kanazawa Univ, Fac Math & Phys, Kanazawa, Ishikawa 9201192 - Japan

^[3] Univ Estadual Paulista, Dept Matemat & Comp, Fac Ciencias & Tecnol, BR-19060900 Presidente Prudente, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: SIAM JOURNAL ON NUMERICAL ANALYSIS; v. 59, n. 6, p. 2955-2988, 2021.
• Citações Web of Science: 0

Resumo

In this work, new finite difference schemes are presented for dealing with the upper convected time derivative in the context of the generalized Lie derivative. The upper-convected time derivative, which is usually encountered in the constitutive equation of the popular viscoelastic models, is reformulated in order to obtain approximations of second-order in time for solving a simplified constitutive equation in one and two dimensions. The theoretical analysis of the truncation errors of the methods takes into account the linear and quadratic interpolation operators based on a Lagrangian framework. Numerical experiments illustrating the theoretical results for the model equation defined in one and two dimensions are included. Finally, the finite difference approximations of second-order in time are also applied for solving a two-dimensional Oldroyd-B constitutive equation subjected to a prescribed velocity field at different Weissenberg numbers. (AU)

• Processo FAPESP: 13/07375-0 - CeMEAI - Centro de Ciências Matemáticas Aplicadas à Indústria
• Beneficiário: Francisco Louzada Neto
• Modalidade de apoio: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs
• Processo FAPESP: 17/11428-2 - Métodos numéricos para escoamentos não-newtonianos com superfícies livres: efeitos da tensão superficial
• Beneficiário: Débora de Oliveira Medeiros
• Modalidade de apoio: Bolsas no Brasil - Doutorado
• Processo FAPESP: 19/08742-2 - Esquemas estabilizantes para resolução de escoamentos viscoelásticos com superfície livre e efeitos de tensão superficial
• Beneficiário: Débora de Oliveira Medeiros
• Modalidade de apoio: Bolsas no Exterior - Estágio de Pesquisa - Doutorado