A New Boundary Condition for Rate-Type Non-Newtonian Diffusive Models and the Stable MAC Scheme

A New Boundary Condition for Rate-Type Non-Newtonian Diffusive Models and the Stable MAC Scheme

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.

Author Details

Kun Li

Youngju Lee

Christina Starkey

  1. Structured backward error analysis for generalized saddle point problems

    Zheng, Bing

    Lv, Peng

    Advances in Computational Mathematics, Vol. 46 (2020), Iss. 2

    https://doi.org/10.1007/s10444-020-09787-x [Citations: 4]