Second-order finite difference approximations of the upper-convected time derivative
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.
Cite
@article{arxiv.2106.02950,
title = {Second-order finite difference approximations of the upper-convected time derivative},
author = {Debora O. Medeiros and Hirofumi Notsu and Cassio M. Oishi},
journal= {arXiv preprint arXiv:2106.02950},
year = {2023}
}