Research

Methods

In this study, I employ Finite Element Method (FEM) utilizing the open-source FEniCS library for numerical simulations in fluid dynamics.

Viscoelastic rate-type fluids

Stabilization Study

The High Weissenberg Number Problem is well-known challenge. In my Diploma thesis, I have implemented generalized Oldroyd-B model with the stress diffusion. I was looking for the steady solution while preserving smallest stress diffusion coefficient as possible. This allowed simulations of flows in the classical benchmark of flow past the cylinder for arbitrary Weissenberg number and I have observed quite interesting behavior. Stay tuned.

Weissenberg effect

While studying a family of Oldroyd-like viscoelastic models, I implemented a simulation of the Weissenberg (Rod-climbing) effect as an axisymmetric problem with a free surface. The following simulation (Time [s], u is mesh deformation) is based on the MIT experiment. We are using the total ALE (Arbitrary Lagrangian Eulerian) method and Nitsche method to address a free surface problem. Specific details may be found in my Diploma thesis. The only drawback is that the simulation crashes before reaching a steady state due to mesh breakage as the fluid bulges in a small area. An update is currently in progress.

The update from my PhD studies has arrived: It has been demonstrated that the rod climbing effect exhibits breathing instability for Weissenberg numbers (We) approximately greater than 1/2. This phenomenon is also observed in our simulation with We = 1 after implementing remeshing. In detail, the fluid climbs up and then folds down, resembling a wave. While this behavior is expected to periodically repeat, our simulation crashes due to self-contact of the mesh (virtual, due to the ALE method, but sufficient). This limitation arises from the methods employed. To address this issue, one could develop a method for assimilating the mesh after contact, or consider alternatives such as level-set methods or focus on meshless methods, e.g., SPH. Nevertheless, keep in mind that total ALE method works very well in reasonable deformations and it is no surprise that self-contact leads to a breakdown as the method requires uniqueness in the deformation mapping.