Simulation of wallbounded turbulent channel flow in the PETSc toolkit

Turbulence modeling is part of the broad scientific field of computational fluid dynamics, or CFD for short. The driving forces behind the research in this field can be roughly recognized into two categories. First, there is the wish for a deeper understanding of the underlying physics behind fluid dynamics. For well over a century now, turbulence has been one of the most intriguing and least understood phenomena in physics. Secondly, because the engineering and medical applications of CFD are numerous, every advance in CFD leading to more accuracy can mean a potential business advantage. There exist many both commercial and academic CFD codes for all kinds of applications. What most of them have in common is that one or more modeling approximations or heuristics have been applied to enable them to deal with real-life problems. DNS can be recognized as the only CFD instrument that does not make assumptions whatsoever about a particular flow. It is therefore considered equally good as (or even better than) real-life experiments. Before the dawn of computers however, doing experiments was the only option available. Physicists set up experiments in order to gain a deeper understanding of fluids and their behavior. For example, Ludwig Prandtl discovered the existence of boundary layers while doing his experiments in 1904. Nowadays, experiments are still a very reliable and valuable tool for engineers in the design process. Probably every car sold in the last 30 years has been tested in a wind-tunnel to monitor its aerodynamic properties. However, experiments this scale require tremendous resources in time, money and technology, which are not always available. Also, for certain types of flow, experiments can only be done in scale (e.g. ships) or not at all (blood flow through the heart). These are examples where CFD is indispensable.