Non-Newtonian rheologies are crucial for modelling flows in both environmental and industrial settings. In particular, the nonsmooth and highly nonlinear characteristics of viscoplastic Bingham or Herschel-Bulkley fluids give rise to numerous analytical and numerical challenges. Previous attempts to overcome these hurdles are hardly convincing: they either lead to computationally inefficient methods, or they solve auxiliary problems instead, which exhibit fundamentally different physical features.

In order to simulate instationary 2D viscoplastic flow both accurately and efficiently, we borrow a range of tools from other disciplines. We combine analytical concepts from optimal control theory and proven discretisation schemes for the Navier-Stokes equations with a cutting-edge algorithm from image processing. This talk will demonstrate how our new approach to viscoplastic fluid flows outperforms present state-of-the-art methods.