Authors
Young-Ju Lee, Jinchao Xu
Publication date
2006/2/1
Journal
Computer methods in applied mechanics and engineering
Volume
195
Issue
9-12
Pages
1180-1206
Publisher
North-Holland
Description
We propose a class of new discretization schemes for solving the rate-type non-Newtonian constitutive equations. The so-called conformation tensor has been known to be symmetric and positive definite in a large class of constitutive equations. Preserving such a positivity property on the discrete level is believed to be crucially important but difficult. High Weissenberg number problems on numerical instabilities have been often associated with this issue. In this paper, we present various discretization schemes that preserve the positive-definiteness of the conformation tensor regardless of the time and spatial resolutions. Moreover, the robustness of the algorithm has been also demonstrated by the stability analysis using the discrete analogue of energy estimates. New schemes presented in this paper are constructed based upon the newly discovered relationship between the rate-type constitutive equations and the …
Total citations
20072008200920102011201220132014201520162017201820192020202120222023202416912133631752234122