
The thermodynamic and fluid dynamic behavior of such flows is dictated by the relations between the Knudsen (Kn), Reynolds (Re) and Mach (Ma) numbers:
 One of the bestknown, scale invariant phenomena in fluid dynamics are turbulent flows. The unsteady character of turbulence is modeled by timeresolved simulations.
Because of the very small length scales of turbulent structures and the restricted refinement possibilities of numerical grids, not all convective motions can be resolved directly.
Therefore subscale formulations obtained through turbulence models are necessary.
 Additional areas of interest are turbulent dispersed flows with boundary layers, turbulent suspension flow with phase transition, problems regarding contact between fluids and solids,
contact line dynamics, stability problems of fluid mixtures (linear and nonlinear), selfgravitating flows and rarefied gases, where a link between fluid and solid mechanics can be established.
 To achieve this, the dynamics of microscale particles and molecules must be modeled. Based on statistical physics the molecular motion is described, among other formulations,
by the Brownian motion. Physical quantities of molecular flows are described through spectral methods as transport equations for the probability density function over the phase space.
Some external applications are biotechnological research activities, regenerative energy systems, filling technology, and meteorological predictions in environmental science.
The main research area, technical fluid flows and combustion, is this way significantly broadened by establishing a link to further research areas.

