Two out of eight new priority programs (SPP) that have been approved by the Senate of the German Research Foundation (DFG) in its most recent meeting will be established at the University of Stuttgart. One of them is the priority program of Prof. Christian Rohde from the Institute of Applied Analysis and Numerical Simulation who is also research coordinator and member of the board of directors of the Stuttgart Cluster of Excellence "Data-integrated Simulation Science". He will mathematically substantiate hypotheses in the field of fluid mechanics and develop a new generation of numerical simulation tools in the group he coordinates.
Priority Program "Hyperbolic Conservation Laws in Fluid Mechanics: Complexity, Scales, Noise (CoScaRa)", Coordinator Prof. Christian Rohde.
A sonic boom, like the one heard over Stuttgart in March, is caused by shock waves in compressible flows. If one wants to mathematically model this effect or other transport processes in the natural sciences and engineering, this often requires systems of hyperbolic partial differential equations such as the Euler equations known from fluid mechanics. More generally, hyperbolic models form the basis of numerical simulations and decisions based on them in many socially relevant issues.
This includes, for example, the computer-based design of aircraft and spacecraft, weather forecasting or aspects of climate research. Despite the fundamental importance of these mathematical models in fluid mechanics, many basic questions about hyperbolic equations are still completely open today.
Against this background, researchers from the fields of mathematics, fluid mechanics and theoretical physics would like to tackle completely new approaches to hyperbolic systems of equations in the SPP "Hyperbolic Conservation Laws in Fluid Mechanics: Complexity, Scales, Noise (CoScaRa)". In addition to the University of Stuttgart, the universities of Mainz and Leipzig, the TU Darmstadt, and the RWTH Aachen participate.
These approaches, previously thought to be impossible, are made possible by new results from theoretical mathematics and discoveries from fluid mechanics that can contribute in particular to understanding the interaction of turbulent flow regimes and shock waves. Specifically, this involves the idea of wild solutions borrowed from geometry (complexity), modern concepts of multiscale modeling (scales), and pioneering stochastic modeling techniques (noise).
As a visionary goal, conjectures on the development and distribution of kinetic energy in turbulent flows, such as the Kolmogorov hypothesis, which have so far only been largely phenomenologically proven, are to be mathematically substantiated. This would also lead to a new generation of numerical simulation tools, which is the goal of the Cluster of Excellence "Data-integrated Simulation Science" (EXC 2075, Simtech) at the University of Stuttgart.