On the absolute instability of semi-implicit schemes for hydrostatic models

[摘要] The dependence of the linear stability of two-time-level finite-difference, semi-implicit schemes on the choice of reference temperature profile is studied. Particular vertical profiles of the temperature are considered to derive analytical conditions of stability. Analysis is made for general form of different model parameters such as the number of vertical levels and their distribution, the time step size, and the values of the viscosity coefficients. The derived conditions of stability are more restrictive than those for three-time-level schemes, but obtained necessary and sufficient condition for constant vertical lapse rates of the temperature has the form frequently applied to three-time-level schemes: the basic temperature profile should be warmer than the actual one. Performed numerical experiments show that the last restriction is neither necessary nor sufficient condition of stability for general temperature profiles. (C) 2007 Elsevier B.V. All rights reserved.

[发布日期] 2008-09-01

[效力级别]  Proceedings Paper

[关键词] atmospheric hydrostatic model;semi-implicit scheme;linear stability