B7.: Variational modeling of non-Newtonian fluids

In many cases, the laminar/turbulent transition is due to modified flows / flow conditions at a length- and time-scale which is far smaller than the ones for the macroscopic fluid problem. To account for this scale-bridging problem, different approaches have been developed, such as Direct Numerical Simulations (DNS), Reynolds-Averaged-Navier-Stokes (RANS) or Large Eddy Simulations (LES).

In this project, a different perspective to the problem shall be investigated. Starting from modeling concepts of solids with evolving microstructure, an additional thermodynamic state variable, referred to as internal variable, is introduced. Then, evaluation of related stationarity principles yields evolution equations for the internal variable for the fluid model. By this, the description of non-Newtonian fluids is possible in a completely novel way. The introduction of internal variables serves as promising approach to reduce the complexity and thus the order of the model.

The additional evolution equation needs to be solved in parallel to the balance of linear momentum. The project thus also covers the development of an efficient numerical treatment for this novel approach for modeling fluids. In total, a novel methodology for the modeling of non-Newtonian fluids shall be developed in this project.

Supervision: Prof. Junker (UH), Prof. Wick (LUH) and Prof. Néron (ENS)