Conservative Finite Volume Schemes for Meteorological Applications

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 near-singular 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 WTG-type limit regimes. The design of the scheme will be motivated by asymptotic considerations as explained in the first two lectures.

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