The master thesis proposes a semi-implicit method for the discretization of the numerical weather prediction model. We present von Neumann's method for stability analysis, which is then used for stability analysis of two-time-level semi-implicit schemes for numerical solving a system of partial differential equations. In this way, we test a non-hydrostatic weather prediction model formulated with new variables describing pseudovertical divergence $\mathbb{D}$ and real pressure $\hat{q}$. We first show the results in a theoretical way, where we are mainly interested in how the orography of the surface over which we forecast the weather affects it, and then we show them for two-dimensional real case experiments, which we do with the model Aladin.
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