The solution of complex rarefied flows with the BGK equation and the Discrete Velocity Method (DVM) requires a large number of velocity grid points leading to significant computational costs. We propose an adaptive velocity grid approach exploiting the fact that locally in space, the distribution function is supported only by a sub-set of the global velocity grid. The velocity grid is adapted thanks to criteria based on local temperature, velocity and on the enforcement of mass conservation. Simulations in 1D and 2D are presented for different Knudsen numbers and compared to a global velocity grid BGK solution, showing the computational gain of the proposed approach.

Various projects to find planets or entire planetary systems around main sequence stars in the solar neighborhood are presently under way. When ELTs will be operational, there will be literally thousands of confirmed planetary systems including spectro-photometric detections. At this point it becomes inevitable to consider the next logical step: the spectroscopic analysis of the atmospheres of these planets. High-resolution spectroscopy, i.e. resolving $v \times \sin (i)$ of these planets, in the wavelength regime of 950-5500nm is a powerful and promising tool. In view of the obvious contrast problems in detecting such planets non-LTE features are specifically targeted. Sensitivity estimates for the detection of the non-thermal OH glow in oxygen-bearing atmospheres are given. With 8m-class telescopes such a search is impossible, but a dedicated spectrograph, e.g. at the projected ESO 100m OWL telescope could detect Earth-like planets at a distance of ${\approx} 10$ parsec. A conceptual design for a dedicated spectrograph, NOCTUA, is presented. In case of ELTs of smaller size the science case changes and the instrument requirements have to be adjusted. Preparatory work with CRIRES, ESO's Cryogenic Infrared Echelle Spectrograph on the VLT at $\frac{\lambda}{\Delta \lambda} \approx 10^5$ as well as other science cases are shortly discussed.