Lagrangian Mesh Model with Regridding for Planar Poiseuille Flow (Communications in Computational Physics, 2019)
Many biological settings involve complex fluids that have non-Newtonianmechanical responses that arise from suspended microstructures. In contrast, Newtonian fluids are liquids or mixtures of a simple molecular structure that exhibit a linearrelationship between the shear stress and the rate of deformation. In modeling complex fluids, the extra stress from the non-Newtonian contribution must be included inthe 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 areused in the comparison of simulation and theoretical results. The Lagrangian meshresults are compared with Oldroyd-B using comparable parameters. A regridding algorithm is introduced for the Lagrangian mesh model. We show that the Lagrangianmesh model simulations with regridding produce results in close agreement with theOldroyd-B model.
Keywords: Lagrangian mesh model; Oldroyd-B; immersed boundary method; viscoelastic fluid; regridding methods.