Study of viscoelastic behavior in an immersed boundary-Lagrangian mesh model

Many biological settings involve complex fluids that have non-Newtonian mechanical responses that arise from suspended microstructures. In this study, we compare Lagrangian mesh and Oldroyd-B formulations of non-Newtonian fluid-structure interaction in an immersed boundary framework. Significantly, we find remeshing, as well as fluid and/or mesh refinement increase the stability and accuracy of Lagrangian mesh simulations and produce results highly comparable with that of the Oldroyd-B model for test cases such as planar Poiseuille flow and Stokes' problems. Further investigations revealed the trade-offs between discretization error and CPU time consumption at various regridding frequencies and determined an optimal regridding interval. In addition, cases are compared at low Reynolds number and a fixed set of parameters including the Weissenberg number and the viscosity ratio. The form of the mesh could be regarded as a coarse grain model of the physical structure of the viscoelastic component of the fluid and, in some contexts, distortion of the mesh may have a physical interpretation and regridding would be unnecessary. Modifications to the models are proposed with viscoelastic links and comparisons with properties of viscoelastic media such as mucus, biological tissues, and biofilms.