New formulations, positivity preserving discretizations and stability analysis for non-newtonian flow models

摘要: 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 large Preserving such positivity property on discrete level is believed crucially important but difficult. High Weissenberg number problems numerical instabilities have often associated with this issue. In paper, we present various that preserve positive-definiteness regardless time spatial resolutions. Moreover, robustness algorithm also demonstrated by stability analysis using analogue energy estimates. New presented paper are constructed based upon newly discovered relationship between equations matrix Riccati differential