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Volume 36, Issue 4
A New Boundary Condition for Rate-Type Non-Newtonian Diffusive Models and the Stable MAC Scheme

Kun Li, Youngju Lee & Christina Starkey

DOI: 10.4208/jcm.1703-m2015-0359

J. Comp. Math., 36 (2018), pp. 605-626.

Published online: 2018-06

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  • Abstract

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.

  • Keywords

Boundary conditions, Diffusive complex fluids models, Positivity preserving schemes, Stability of the MAC schemes.

  • AMS Subject Headings

15A15, 15A09, 15A23

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

galoispure@gmail.com (Kun Li)

yjlee@txstate.edu (Youngju Lee)

cs1721@txstate.edu (Christina Starkey)

  • BibTex
  • RIS
  • TXT
@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 = {

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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1703-m2015-0359}, url = {http://global-sci.org/intro/article_detail/jcm/12308.html} }
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 -

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.

Li , KunLee , Youngju and Starkey , Christina. (2018). A New Boundary Condition for Rate-Type Non-Newtonian Diffusive Models and the Stable MAC Scheme . Journal of Computational Mathematics. 36 (4). 605-626. doi:10.4208/jcm.1703-m2015-0359
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