A reasonable numerical treatment of multiscale problems is a challenging task due the complex interaction of the various time and length scales. All these length scales are often not representable on a discrete numerical grid due to restricted computational power. Even if a detailed simulation is feasible, sometimes a quick answer is needed or problem parameters have to be varied systematically.
A modeler's life becomes even more complicated when flows exhibit thin internal boundary layers of large activity, e.g., sharp temperature or concentration gradients, laminar/turbulent interfaces, or stiff chemical source terms. In these cases standard CFD tools normally fail, since they cannot resolve the layer physics due to insufficient grid resolution. Even elaborate physically based subgrid models are than numerically smeared out, so that a distinction between numerical (e.g.
discretization errors) and physical effects (e.g. entrainment) is impossible.
The subtile small scale interaction of molecular effects and turbulence might only be accessed using direct numerical simulation (DNS) and stochastic turbulence models.
In the talk we will sketch the idea of a heterogeneous multiscale ansatz including a possible geometrical representation of thin layers.
Interdisciplinary examples of the concept will be the modeling of thermoacoustic instabilities in combustion devices, radiatively induced buoyancy reversal in a tank, and the modeling of the cloud-topped boundary layer.
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