Scientific Computing and Applied & Industrial Mathematics: Timm Treskatis

What if we could imitate spider silk glands to produce biodegradable materials with properties similar to rubber or plastic? In our interdisciplinary team of fluid dynamicists, chemical engineers and material scientists, my role as mathematician is to try and answer this question from the numerical perspective. In this context, I am working on a problem of multiphase flow that includes advection, diffusion, chemical reaction, osmosis and viscoplastic behavior.

When it comes to the numerical solution of such a model that is based on a real-life problem, I am a strong advocate of so-called mimetic methods, i.e. discretisation schemes which preserve the physical properties of the system also at the discrete level. Following this philosophy, * the transition between viscous flow and plastic creep is treated in a genuinely nonsmooth fashion and not simply smoothed out, * the discretisation of the Navier-Stokes equations is pressure-robust, * conservation of mass and momentum are respected, * maximum principles are preserved, * numerical diffusion is limited to an absolute minimum.

Additionally, the algorithm should clearly be stable, efficient and accurate for both steady and unsteady flow problems.

In this talk, I will show how we can couple fast algorithms from convex optimisation, a finite-element discretisation and algebraic flux correction to attain these objectives. Some videos of various flow configurations are included as well!