Estimation of topography constraints on the numerical stability of a mountain wave simulation

A three-dimensional nonhydrostatic meteorological model is applied to modeling of mountain waves. Numerical schemes with central differences in time and space on staggered grids are used at the so-called "adjustment" time integration stage. These schemes, being unconditionally stable for plane topography, are shown to be only conditionally stable for steep topography. The mountain steepness limitations necessary for numerical stability are obtained by solving numerically the amplification matrix eigenvalue problem.