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Lagrangian Mesh Model with Regridding for Planar Poiseuille Flow

Part of:Physiological, cellular and medical topicsCoupling of solid mechanics with other effectsPartial differential equations, initial value and time-dependent initial-boundary value problemsSpecial subfields of solid mechanicsNumerical methodsBiological fluid mechanics

Published online by Cambridge University Press:  03 May 2017

Jingxuan Zhuo,
Ricardo Cortez and
Robert Dillon
Jingxuan Zhuo*
Affiliation:
Department of Mathematics and Statistics, Washington State University, USA
Ricardo Cortez*
Affiliation:
Department of Mathematics, Tulane University, USA
Robert Dillon*
Affiliation:
Department of Mathematics and Statistics, Washington State University, USA
*
*Corresponding author. Email addresses:jxzhuo@hotmail.com (J. Zhuo), rcortez@tulane.edu (R. Cortez), dillon@math.wsu.edu (R. Dillon)
*Corresponding author. Email addresses:jxzhuo@hotmail.com (J. Zhuo), rcortez@tulane.edu (R. Cortez), dillon@math.wsu.edu (R. Dillon)
*Corresponding author. Email addresses:jxzhuo@hotmail.com (J. Zhuo), rcortez@tulane.edu (R. Cortez), dillon@math.wsu.edu (R. Dillon)

Abstract

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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 Oldfoyd-B model.

Keywords

Lagrangian mesh modelOldroyd-Bimmersed boundary methodviscoelastic fluidregridding methods

MSC classification

Secondary:74F10: Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)76Z05: Physiological flows65M06: Finite difference methods92C10: Biomechanics74S20: Finite difference methods74L15: Biomechanical solid mechanics

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 22 , Issue 1 , July 2017, pp. 112 - 132
Copyright
Copyright © Global-Science Press 2017 

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