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Volume 11, Issue 1
A Numerical Study of Multiple Solutions for Laminar Flows in a Porous and Moving Channel

Fen Wang, Ping Lin, Lin Li & Yongyue Jiang

DOI: 10.4208/nmtma.2018.m1604

Numer. Math. Theor. Meth. Appl., 11 (2018), pp. 74-91.

Published online: 2018-11

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  • Abstract

In this paper, based on the finite element formulation, we focus on multiple solutions and their evolution with time for a laminar flow in a permeable channel with expanding or contracting walls. Both Newtonian fluid and micropolar fluid are considered. For the Newtonian fluid model, we find that the profile of the unique solution in the case of injection remains the same for long time, which indicates that the solution may be stable. On the other hand, in the case of large suction, the profile of multiple solutions changes in time, which suggests that the multiple solutions may be unstable. Similar behaviors and conclusions are observed for the micropolar fluid model under different boundary parameters.

  • Keywords

Newtonian fluid, micropolar fluid, multiple solutions, finite element method, bvp4c.

  • AMS Subject Headings

34A99, 35A22, 35K15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-11-74, author = {Fen Wang, Ping Lin, Lin Li and Yongyue Jiang}, title = {A Numerical Study of Multiple Solutions for Laminar Flows in a Porous and Moving Channel}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2018}, volume = {11}, number = {1}, pages = {74--91}, abstract = {

In this paper, based on the finite element formulation, we focus on multiple solutions and their evolution with time for a laminar flow in a permeable channel with expanding or contracting walls. Both Newtonian fluid and micropolar fluid are considered. For the Newtonian fluid model, we find that the profile of the unique solution in the case of injection remains the same for long time, which indicates that the solution may be stable. On the other hand, in the case of large suction, the profile of multiple solutions changes in time, which suggests that the multiple solutions may be unstable. Similar behaviors and conclusions are observed for the micropolar fluid model under different boundary parameters.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2018.m1604}, url = {http://global-sci.org/intro/article_detail/nmtma/10644.html} }
TY - JOUR T1 - A Numerical Study of Multiple Solutions for Laminar Flows in a Porous and Moving Channel AU - Fen Wang, Ping Lin, Lin Li & Yongyue Jiang JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 74 EP - 91 PY - 2018 DA - 2018/11 SN - 11 DO - http://doi.org/10.4208/nmtma.2018.m1604 UR - https://global-sci.org/intro/article_detail/nmtma/10644.html KW - Newtonian fluid, micropolar fluid, multiple solutions, finite element method, bvp4c. AB -

In this paper, based on the finite element formulation, we focus on multiple solutions and their evolution with time for a laminar flow in a permeable channel with expanding or contracting walls. Both Newtonian fluid and micropolar fluid are considered. For the Newtonian fluid model, we find that the profile of the unique solution in the case of injection remains the same for long time, which indicates that the solution may be stable. On the other hand, in the case of large suction, the profile of multiple solutions changes in time, which suggests that the multiple solutions may be unstable. Similar behaviors and conclusions are observed for the micropolar fluid model under different boundary parameters.

Fen Wang, Ping Lin, Lin Li and Yongyue Jiang. (2018). A Numerical Study of Multiple Solutions for Laminar Flows in a Porous and Moving Channel. Numerical Mathematics: Theory, Methods and Applications. 11 (1). 74-91. doi:10.4208/nmtma.2018.m1604
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