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Volume 22, Issue 1
Lagrangian Mesh Model with Regridding for Planar Poiseuille Flow

Jingxuan Zhuo, Ricardo Cortez & Robert Dillon

DOI: 10.4208/cicp.OA-2016-0109

Commun. Comput. Phys., 22 (2017), pp. 112-132.

Published online: 2019-10

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  • Abstract

Many biological settings involve complex fluids that have non-Newtonian mechanical responses that arise from suspended microstructures. In contrast, Newtonian fluids are liquids or mixtures of a simple molecular structure that exhibit a linear relationship between the shear stress and the rate of deformation. In modeling complex fluids, the extra stress from the non-Newtonian contribution must be included in the governing equations.
In this study we compare Lagrangian mesh and Oldroyd-B formulations of fluid-structure interaction in an immersed boundary framework. The start-up phase of planar Poiseuille flow between two parallel plates is used as a test case for the fluid models. For Newtonian and Oldroyd-B fluids there exist analytical solutions which are used in the comparison of simulation and theoretical results. The Lagrangian mesh results are compared with Oldroyd-B using comparable parameters. A regridding algorithm is introduced for the Lagrangian mesh model. We show that the Lagrangian mesh model simulations with regridding produce results in close agreement with the Oldroyd-B model.

  • Keywords

Lagrangian mesh model, Oldroyd-B, immersed boundary method, viscoelastic fluid, regridding methods.

  • AMS Subject Headings

74F10, 76Z05, 65M06, 92C10, 74S20, 74L15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

jxzhuo@hotmail.com (Jingxuan Zhuo)

rcortez@tulane.edu (Ricardo Cortez)

dillon@math.wsu.edu (Robert Dillon)

  • BibTex
  • RIS
  • TXT
@Article{CiCP-22-112, author = {Zhuo , JingxuanCortez , Ricardo and Dillon , Robert}, title = {Lagrangian Mesh Model with Regridding for Planar Poiseuille Flow}, journal = {Communications in Computational Physics}, year = {2019}, volume = {22}, number = {1}, pages = {112--132}, abstract = {

Many biological settings involve complex fluids that have non-Newtonian mechanical responses that arise from suspended microstructures. In contrast, Newtonian fluids are liquids or mixtures of a simple molecular structure that exhibit a linear relationship between the shear stress and the rate of deformation. In modeling complex fluids, the extra stress from the non-Newtonian contribution must be included in the governing equations.
In this study we compare Lagrangian mesh and Oldroyd-B formulations of fluid-structure interaction in an immersed boundary framework. The start-up phase of planar Poiseuille flow between two parallel plates is used as a test case for the fluid models. For Newtonian and Oldroyd-B fluids there exist analytical solutions which are used in the comparison of simulation and theoretical results. The Lagrangian mesh results are compared with Oldroyd-B using comparable parameters. A regridding algorithm is introduced for the Lagrangian mesh model. We show that the Lagrangian mesh model simulations with regridding produce results in close agreement with the Oldroyd-B model.

}, issn = {1991-7120}, doi = {https://doi.org/ 10.4208/cicp.OA-2016-0109}, url = {http://global-sci.org/intro/article_detail/cicp/13349.html} }
TY - JOUR T1 - Lagrangian Mesh Model with Regridding for Planar Poiseuille Flow AU - Zhuo , Jingxuan AU - Cortez , Ricardo AU - Dillon , Robert JO - Communications in Computational Physics VL - 1 SP - 112 EP - 132 PY - 2019 DA - 2019/10 SN - 22 DO - http://doi.org/ 10.4208/cicp.OA-2016-0109 UR - https://global-sci.org/intro/article_detail/cicp/13349.html KW - Lagrangian mesh model, Oldroyd-B, immersed boundary method, viscoelastic fluid, regridding methods. AB -

Many biological settings involve complex fluids that have non-Newtonian mechanical responses that arise from suspended microstructures. In contrast, Newtonian fluids are liquids or mixtures of a simple molecular structure that exhibit a linear relationship between the shear stress and the rate of deformation. In modeling complex fluids, the extra stress from the non-Newtonian contribution must be included in the governing equations.
In this study we compare Lagrangian mesh and Oldroyd-B formulations of fluid-structure interaction in an immersed boundary framework. The start-up phase of planar Poiseuille flow between two parallel plates is used as a test case for the fluid models. For Newtonian and Oldroyd-B fluids there exist analytical solutions which are used in the comparison of simulation and theoretical results. The Lagrangian mesh results are compared with Oldroyd-B using comparable parameters. A regridding algorithm is introduced for the Lagrangian mesh model. We show that the Lagrangian mesh model simulations with regridding produce results in close agreement with the Oldroyd-B model.

Zhuo , JingxuanCortez , Ricardo and Dillon , Robert. (2019). Lagrangian Mesh Model with Regridding for Planar Poiseuille Flow. Communications in Computational Physics. 22 (1). 112-132. doi: 10.4208/cicp.OA-2016-0109
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