Medeiros, Debora D.Notsu, HirofumiOishi, Cassio M. [UNESP]2022-04-282022-04-282021-01-01Siam Journal On Numerical Analysis. Philadelphia: Siam Publications, v. 59, n. 6, p. 2955-2988, 2021.0036-1429http://hdl.handle.net/11449/218786In 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.2955-2988enggeneralized Lie derivativeLagrangian schemefinite difference methodArtigo10.1137/20M1364990WOS:000748784400007