A semi-implicit compressible model for atmospheric flows with seamless access to soundproof and hydrostatic dynamics
Tommaso Benacchio, Rupert Klein
TL;DR
This paper presents a second-order numerical scheme for atmospheric flows that seamlessly integrates soundproof and hydrostatic dynamics, enabling larger time steps and improved efficiency for small to planetary scale simulations.
Contribution
The authors develop a semi-implicit, second-order finite volume scheme that unifies compressible, soundproof, and hydrostatic models within a single framework, allowing flexible and efficient atmospheric simulations.
Findings
Scheme is competitive on nonhydrostatic and hydrostatic benchmarks.
Large time step capability demonstrated on planetary inertia-gravity wave test.
Seamless switching between soundproof and hydrostatic modes achieved.
Abstract
We introduce a second-order numerical scheme for compressible atmospheric motions at small to planetary scales. The collocated finite volume method treats the advection of mass, momentum, and mass-weighted potential temperature in conservation form while relying on Exner pressure for the pressure gradient term. It discretises the rotating compressible equations by evolving full variables rather than perturbations around a background state, and operates with time steps constrained by the advection speed only. Perturbation variables are only used as auxiliary quantities in the formulation of the elliptic problem. Borrowing ideas on forward-in-time differencing, the algorithm reframes the authors' previously proposed schemes into a sequence of implicit midpoint, advection, and implicit trapezoidal steps that allows for a time integration unconstrained by the internal gravity wave speed.…
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