Modeling, Simulation and Optimization of Complex and Extreme Flows

Many real world applications in fluid mechanics include either complex flows where the assumptions of linear standard models are not given, or such extreme conditions that the capability of current numerical methods is reached or exceeded.

Materials like oil, lubricants, bitumen or ice-layer show a strongly nonlinear behavior and can completely change their characteristics when undergoing large pressure and stresses. Many problems require the consideration of coupled processes, where the fluid interacts with rigid or elastic solids, particles or other liquids.

The mathematical description of all these processes is a challenge. Typical applications often include large problem data and no smallness assumptions of parameters can be made. This makes existence and uniqueness results not available or extremely hard to get. Discretization results in very stiff algebraic systems, such that standard solver techniques mostly fail. Strong nonlinearities complicate the use of gradient based techniques needed for error estimation or optimization.

In this minisymposium, we will bring together scientists dealing with all kinds of complex flows, that have in common that standard methods in analysis, discretization and optimization are not applicable and the development of new techniques is needed.