TY - JOUR
T1 - A New Boundary Condition for Rate-Type Non-Newtonian Diffusive Models and the Stable MAC Scheme 
AU - Li , Kun
AU - Lee , Youngju
AU - Starkey , Christina
JO - Journal of Computational Mathematics
VL - 4
SP - 605
EP - 626
PY - 2018
DA - 2018/06
SN - 36
DO - http://doi.org/10.4208/jcm.1703-m2015-0359
UR - https://global-sci.org/intro/article_detail/jcm/12308.html
KW - Boundary conditions, Diffusive complex fluids models, Positivity preserving schemes, Stability of the MAC schemes.
AB - <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>