Volume 29, Issue 6

New algorithms for statistical modelling of radiation transfer through stochastic exponentially correlated media are constructed. For this purpose, a special geometrical implementation of the ‘maximum cross-section method’ is developed, which allows us to take into account the absorption of radiation with a weight exponential factor. Asymptotic estimates of the parameters of the homogenized radiation model are constructed relative to the size of the medium. A special ‘distributive’ method of pseudo-random numbers generation used in the paper allows us to perform a comparative analysis of simulation results on the base of the corresponding correlation of statistical estimates.

An optimal splitting technique is proposed for numerical solution of the Euler and Navier-Stokes equations for a compressible heat-conducting gas. This technique is common for original equations in the divergent and nondivergent form. Based on this splitting, a class of economical (in the number of operations per a grid node) difference schemes is proposed so that those schemes are implemented on fractional steps by the scalar sweep methods and have a large stability margin, but have a lesser number of sweep steps in their implementation.

The paper presents a new version of the three-dimensional model of general circulation of Earth troposphere-stratosphere-mesosphere (for altitudes up to 90 km from the surface) with a hybrid vertical coordinate. A method of vertical discretization is developed according to the numerical algorithms and preserving the equivalence of algorithms used in previous models. An algorithm of semi-implicit integration in time is proposed. The new version of the model adequately represents climatic characteristics,which are confirmed by comparison of the results of numerical experiments with observation data and with the previous version of the atmospheric circulation model using sigma-coordinates.

A numerical stochastic model of spatio-temporal inhomogeneous fields of daily sums of liquid precipitation is considered in the paper on regular and irregular grids. The approach to modelling inhomogeneous fields is based on stochastic interpolation of fields from weather stations to grid points.