
Conservative Finite Volume Schemes for Meteorological Applications
Rupert Klein
Potsdam Institute for Climate Impact Research
Abstract
The emergence of simplified limit equations from asymptotic (or scale)
analyses of the full compressible flow equations is typically associated
with singular mathematical limits. The transition from compressible
to incompressible or anelastic flows is a prominent example. Such
singular limit regimes give rise to considerable computational
difficulties when a solver for a general set of flow equations is
applied in a nearsingular flow regime. This lecture presents recent
efforts to develop a numerical scheme for the full compressible flow
equations in conservation form which properly captures both the
classical anelastic, and the WTGtype limit regimes. The design of
the scheme will be motivated by asymptotic considerations as explained
in the first two lectures.
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