Abstract: Current research on transitional and turbulent flows mainly relies on experiments, either in a wind tunnel, or increasingly also as virtual experiments in a computer. High-fidelity computational fluid dynamics (CFD) has become feasible only during the last decades, mainly due to the prohibitive cost for well-resolved simulations of turbulent flows. In the first part of this talk, we will discuss selected aspects of high-order spectral methods applied to fluids problems, including accuracy, robustness, as well as modern features such as parallel scaling and adaptive meshes.
Wall-bounded turbulence emerges e.g. along the surface of moving objects such as airplanes or inside pipelines, and is the main cause of drag exerted on those bodies. It is exactly these two generic configurations that we will discuss in more detail during the second part. i) The flow through pipes with a bend (i.e. curved pipe flow) offers one additional defining parameter, which unlocks a wonderful physical complexity: not only is the pipe flow linearly unstable, it also shows peculiar co-existence of laminar and turbulent flow. Even turbulence in bent pipes is quite different: clear low-frequency oscillations are present which yet need to be understood. ii) The external turbulent flow along wing profiles is subjected to both favorable and adverse pressure gradients, which modify the flow profiles considerably; our current understanding is only empirical. We will review a few of our latest results for this configuration, and discuss aspects of practical relevance, e.g. the possibility of flow control under these circumstances, and address the question of accuracy when measuring very close to solid walls by so-called cavity probes. Finally, we will look at some more recent numerical methods applied to aeronautical flows, i.e. Gaussian process regression and multifidelity simulations, that may allow for potentially great improvements of simulation capabilities.