Stability of Leapfrog Constant-Coefficients Semi-Implicit Schemes for the Fully Elastic System of Euler Equations: Flat-Terrain Case

The stability of semi-implicit schemes for the hydrostatic primitive equations system has been studied extensively over the past 20 yr, since this temporal scheme and this system represented a standard for NWP. However, with the increase of computational power, the relaxation of the hydrostatic approximation through the use of nonhydrostatic fully elastic systems is now emerging for future NWP as an attractive solution valid at any scale. In this context, several models employing the so-called Euler equations together with a constantcoefficients semi-implicit time discretization have already been developed, but no solid justification for the suitability of this algorithmic combination has been presented so far, especially from the point of view of robustness.