Year: 2018
Author: Kun Li, Youngju Lee, Christina Starkey
Journal of Computational Mathematics, Vol. 36 (2018), Iss. 4 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1703-m2015-0359
Journal of Computational Mathematics, Vol. 36 (2018), Iss. 4 : pp. 605–626
Published online: 2018-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Boundary conditions Diffusive complex fluids models Positivity preserving schemes Stability of the MAC schemes.