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We introduce a second-order numerical scheme for compressible atmosphericmotions at small to planetary scales. The collocated finite volume methodtreats the advection of mass, momentum, and mass-weighted potential temperaturein conservation form while relying on Exner pressure for the pressure gradientterm. It discretises the rotating compressible equations by evolving fullvariables rather than perturbations around a background state, and operateswith time steps constrained by the advection speed only. Perturbation variablesare only used as auxiliary quantities in the formulation of the ellipticproblem. Borrowing ideas on forward-in-time differencing, the algorithmreframes the authors' previously proposed schemes into a sequence of implicitmidpoint, advection, and implicit trapezoidal steps that allows for a timeintegration unconstrained by the internal gravity wave speed. Compared withexisting approaches, results on a range of benchmarks of nonhydrostatic- andhydrostatic-scale dynamics are competitive. The test suite includes a newplanetary-scale inertia-gravity wave test highlighting the properties of thescheme and its large time step capabilities. In the hydrostatic-scale cases themodel is run in pseudo-incompressible and hydrostatic mode with simpleswitching within a uniform discretization framework. The differences with thecompressible runs return expected relative magnitudes. By providing seamlessaccess to soundproof and hydrostatic dynamics, the developments represent anecessary step towards an all-scale blended multimodel solver.

A semi-implicit compressible model for atmospheric flows with seamless access to soundproof and hydrostatic dynamics