Non-hydrostatic modelling

The ALADIN-NH dynamical core, which is at the heart of AROME, has been a major project from 1993 to 2005 between Météo-France and the ALADIN cosrtium. It has lead to some very competitive model numerics that work particularly well at kilometric resolutions, with a timestep vastly superior to those used by competing NH models. It has been adopted by the HIRLAM consortium as the basis for its next generation model, and it is being considered by ECMWF as a long-term basis for future high resolution global modelling.

References

The online Aladin-NH dynamical core documentation (copied from the main GMAP documentation site, section 'Dynamics')
Bénard, P. , J. Masek, and J. Vivoda, 2005: Stability of leap-frog constant-coefficients semi-implicit schemes for the fully elastic system of Euler equations. Case with orography. Mon. Wea. Rev, 133, pp.1065-1075.
Bénard, P., R. Laprise, J. Vivoda, P. Smolikovà, 2004: Stability of Leap-Frog Constant-Coefficients Semi-Implicit Schemes for the Fully Elastic System of Euler Equations. Flat-Terrain Case. Mon. Wea. Rev., 132, pp. 1306-1318.
Bénard, P., 2004: On the Use of a Wider Class of Linear Systems for the Design of Constant-Coefficients Semi-Implicit Time-Schemes in NWP. Mon. Wea. Rev, 132, pp. 1319-1324.
Bénard, P., 2004: ALADIN-NH/AROME dynamical core: status and possible extension to IFS. Proceedings of ECWMF Seminar on "Recent developments in numerical methods for atmosphere and ocean modelling", 6-10 Sept 2004, Reading U.K. Available in the ECMWF library.
Bénard, P., 2003: Stability of Semi-Implicit and Iterative Centred-Implicit Time Discretisations for various Equation Systems Used in NWP. Mon. Wea. Rev., 131, pp 2479-2491.
Geleyn, J.F. and R. Bubnova, 1997: The fully-elastic equations cast in hydrostatic-pressure coordinate: accuracy and stability aspects of the scheme as implemented in ARPEGE/ ALADIN. Atmosphère Océan, pp.261-278.
Bubnova, R., G. Hello, P. Bénard and J.-F. Geleyn, 1995: Integration of the fully-elastic equations cast in the hydrostatic pressure terrain-following coordinate in the framework of the ARPEGE/ALADIN NWP system. Mon. Wea. Rev., 123, pp.515-535.