Medeiros, Debora D.
Oishi, Cassio M.
Total Authors: 3
 Univ Sao Paulo, Dept Matemat Aplicada & Estat, Inst Ciencias Matemat & Comp ICMC, Campus Sao Carlos, BR-1025480 Sao Paulo, SP - Brazil
 Kanazawa Univ, Fac Math & Phys, Kanazawa, Ishikawa 9201192 - Japan
 Univ Estadual Paulista, Dept Matemat & Comp, Fac Ciencias & Tecnol, BR-19060900 Presidente Prudente, SP - Brazil
Total Affiliations: 3
SIAM JOURNAL ON NUMERICAL ANALYSIS;
Web of Science Citations:
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)