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.