Matrix analysis
Semi-Lagrangian semi-implicit space splitting regional baroclinic atmospheric model
Applied Numerical Mathematics - Applied and computational mathematics: Selected papers of the third panamerican workshop Trujillo, Peru, 24-28 April 2000
On the absolute instability of semi-implicit schemes for hydrostatic models
Journal of Computational and Applied Mathematics
Stability of semi-implicit atmospheric models with respect to the reference temperature profile
NMA'06 Proceedings of the 6th international conference on Numerical methods and applications
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The linear stability of three-time-level finite-difference semi-implicit schemes is studied for hydrostatic atmospheric models with viscosity terms. The main objective is the investigation of stability dependence on choice of reference temperature profile. Characteristic equation for amplification factor is derived in the case of simplified baroclinic atmospheric numerical model, keeping the implicit approximation for the basic temperature profile and explicit approximation for its deviations. Analytical solutions for amplification factor are found in some special cases and computational experiments are performed for different values of model parameters, such as vertical discretization (number of levels and its distribution), temperature profile (basic and actual), and time step. The influence of the viscosity terms on scheme stability is also studied. Performed analysis confirms two main results obtained numerically in other models: instability generated by inappropriate determination of temperature profile is absolute and computational stability can be recovered if the basic reference profile is chosen to be warmer than the actual one.