Tuning the Immersed boundary-Lagrangian mesh model for viscoelastic suspensions

Naturally occurring viscoelastic fluid media such as blood and DNA suspensions are hosts to different types of swimmers and vesicles. The non-Newtonian mechanical responses that arise from suspended microstructures require modification to the immersed boundary framework in order to capture the underlying physics. In the current study, we have extended the Oldroyd-B and Lagrangian mesh formulations to study the viscoelastic behavior of vesicles and swimmers. The models are benchmarked with analytical results where we see that remeshing increases the stability and accuracy of Lagrangian mesh simulations and produces results highly comparable with that of the Oldroyd-B model. Depending on the context, distortion of the Lagrangian mesh can be taken as a coarse grain model of the physical structure of the viscoelastic component of the fluid and regridding would be unnecessary. Further modifications include the implementation of a penalty model that allows us to model bodies that are not neutrally buoyant along with changes in the viscoelastic links that can mimic biological tissues.