Gas Dynamics
For the most technical processes, the motion of fluids is well described by continuum models, such as the Navier-Stokes equations. This is the case because under those common macroscopic conditions the fluid particles interact much more often among each other than with the surfaces, interfaces and boundaries of the fluid. If this situation changes, e.g. because the mean free path of the particles becomes very large or because characteristic flow lengths become very small, classical continuum models make wrong predictions of the flow fields. These rarefied flows are well described by the Boltzmann equation. Numerical methods to solve this integro-differential equation are well known for some time now.
In the transition regime, however, where we have a flow situation where a description by the Navier-Stokes equations does not suffice but a description by the full Boltzmann equation does not seem adequate, there is a gap in our ability to make theoretical predictions of flow conditions based on numerical simulations. This is because the well-understood continuum models do not hold any longer, but solution of the Boltzmann equation requires too expensive numerical effort. The rarefied regime, however plays an important role e.g. in the development of Microscopic Electro-Mechanical Systems where flow conditions can change between the continuum regime and the rarefied regime, like for read/write heads of hard disk drives.
Our research aims at theoretical descriptions and numerical methods that could be used to implement methods that not only allow for adaptation of the numerical solver to the flow fields, but eventually also to adapt the details of the physical model to the particular flow regime.