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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

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

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Author(s):
Medeiros, Debora D. [1] ; Notsu, Hirofumi [2] ; Oishi, Cassio M. [3]
Total Authors: 3
Affiliation:
[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
Total Affiliations: 3
Document type: Journal article
Source: SIAM JOURNAL ON NUMERICAL ANALYSIS; v. 59, n. 6, p. 2955-2988, 2021.
Web of Science Citations: 0
Abstract

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)

FAPESP's process: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry.
Grantee:Francisco Louzada Neto
Support Opportunities: Research Grants - Research, Innovation and Dissemination Centers - RIDC
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
FAPESP's process: 19/08742-2 - Stabilization schemes for solving viscoelastic free surface flows with surface tension effects.
Grantee:Débora de Oliveira Medeiros
Support Opportunities: Scholarships abroad - Research Internship - Doctorate