Colloquium Mathematics-Weiyan Song

Title:
Matrix-based techniques for (flow)-transition studies

Abstract:
Knowledge of flow behavior is getting more and more important in industrial design, air- and spacecraft development, medicine, and civil projects. The difficulty of flows lies in its nonlinear behavior, i.e., in general, the flow does not vary linearly with the forcing and may even change its behavior completely when the forcing is increased. Such changes are called transitions and can be studied by varying parameters in a numerical flow simulation package. This process is called continuation.
In our case, we are interested in first transitions, e.g., a steady flow becoming time-dependent, or a heat conducting flow at rest becoming a convective flow. In many of these cases, we have to deal with steady flows, and we can do with continuation of steady states. However, many simulation codes can only obtain steady states by long time integrations. This is because solving the steady state flow equations at once is numerically difficult. However, in the last decades, steady-state solvers emerged. The problem with these solvers is their limited robustness. During the Ph.D. projects of de Niet and Thies also a solver has been developed in Groningen. The purpose of my thesis was to evaluate how some of these matrix based methods do on a number of classical flow problems

In the presentation, I will briefly explain our methodology and show results on a variety of flow problems and a Turing problem.