Data accompanying the paper "Stability properties of the constant coefficients semi-implicit time schemes solving equation system with controlled nonhydrostatism", submitted to Monthly Weather Review. Each vertical slice experiment has its own ASCII file containing grid point number, vertical height [km], vertical velocity [m/s] and named exp+3000_w_NH.gmt for the non-linear non-hydrostatic flow over a hill with grid spacing of 80m and the time step of 2s, and containing grid point number, vertical height [km], potential temperature [K] and named exp+rng_theta.gmt for the Straka density current experiments with grid spacing of 25m and time step of 1s (with rng=0300, 0600, 0900). The names of experiments and their descriptions are as follows: NLNH flow over a hill Experiment Description Time scheme NL50 nonhydrostatic PC NK66 pabe(5,1) SETTLS NK50 hydrostatic SETTLS NL59 pad(0.1,0.1) SETTLS NK58 pad(0.01,0.01) SETTLS NK59 pad(0.001,0.001) SETTLS Straka test Experiment Description Time scheme SH81 nonhydrostatic PC SH71 pabe(5,1) SETTLS SH72 pad(0.1,0.1) SETTLS SH73 pad(0.01,0.01) SETTLS SH74 pad(0.01,0.01) SETTLS SH75 hydrostatic SETTLS For the vertical cross sections from 3D simulations each experiment has its own ASCII file named exp+rng_vv.gmt containing point number, pressure[hPa], vertical velocity [m/s]. The names of experiments and their descriptions are as follows: 3D simulations, vertical cross sections Experiment Description Time scheme Lee waves K801 nonhydrostatic PC time step=90s K842 pad[0.2,0.2] SETTLS rng=0011 K826 pad[2,1] SETTLS K800 hydrostatic SETTLS Occitania B003 nonhydrostatic, gamma*=3.5 PC time step=15s B249 pad[0.5,0.5], gamma*=5.5 SETTLS rng=0012 B256 pad[0.1,0.1], gamma*=3.5 SETTLS B303 hydrostatic SETTLS

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