@Article{JCM-36-605,
author = {Li , KunLee , Youngju and Starkey , Christina},
title = {A New Boundary Condition for Rate-Type Non-Newtonian Diffusive Models and the Stable MAC Scheme },
journal = {Journal of Computational Mathematics},
year = {2018},
volume = {36},
number = {4},
pages = {605--626},
abstract = {<p style="text-align: justify;">We present a new Dirichlet boundary condition for the rate-type non-Newtonian diffusive
constitutive models. The newly proposed boundary condition is compared with
two such well-known and popularly used boundary conditions as the pure Neumann condition
[1] and the Dirichlet condition by Sureshkumar and Beris [2]. Our condition is demonstrated
to be more stable and robust in a number of numerical test cases. A new Dirichlet
boundary condition is implemented in the framework of the finite difference Marker and
Cell (MAC) method. In this paper, we also present an energy-stable finite difference MAC
scheme that preserves the positivity for the conformation tensor and show how the addition
of the diffusion helps the energy-stability in a finite difference MAC scheme-setting.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1703-m2015-0359},
url = {http://global-sci.org/intro/article_detail/jcm/12308.html}
}