Rupert Klein |
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Well-balanced and scale-dependent time integration and for weakly compressible (atmospheric) flows
Abstract:
Atmospheric flows feature a cascade of characteristic
scales induced by the presence of several independent small
dimensionless parameters in the governing equations. The most
important ones are the Mach, Froude, and Rossby numbers. Depending
on the length and time scales considered, different asymptotic
limit regimes prevail, leading to very different typical flow
behavior, as revealed by single-scale asymptotic analysis. The
development of numerical schemes for the full three-dimensional
compressible flow equations that properly respect such balances
in each individual regime has a considerable history.
Current super-computers allow atmospheric modellers to resolve a broad range of these scales in one and the same simulation. The numericist is thus challenged to devise numerical integrators that simultaneously respect the asymptotic balances across all length and time scale combinations that arise in a particular flow case.
In the first part of this presentation I will introduce the asymptotic characterization of scale-dependent atmospheric flow regimes. In the second part, I discuss recent developments towards related multi-scale time integrators.