A semi-implicit compressible model for atmospheric flows with seamless access to soundproof and hydrostatic dynamics
This work advances numerical weather prediction and climate modeling by enabling efficient, all-scale atmospheric simulations with a unified solver that bridges compressible, soundproof, and hydrostatic regimes.
The authors introduce a second-order numerical scheme for compressible atmospheric flows that operates with time steps constrained only by advection speed, not internal gravity wave speed. The scheme achieves competitive results on benchmarks from nonhydrostatic to planetary scales and provides seamless access to soundproof and hydrostatic dynamics within a uniform framework.
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. Compared with existing approaches, results on a range of benchmarks of nonhydrostatic- and hydrostatic-scale dynamics are competitive. The test suite includes a new planetary-scale inertia-gravity wave test highlighting the properties of the scheme and its large time step capabilities. In the hydrostatic-scale cases the model is run in pseudo-incompressible and hydrostatic mode with simple switching within a uniform discretization framework. The differences with the compressible runs return expected relative magnitudes. By providing seamless access to soundproof and hydrostatic dynamics, the developments represent a necessary step towards an all-scale blended multimodel solver.