Volume 31, Issue 3

A methodology of efficient homogenization of a radiation model for a stochastic media is developed. In this connection, ‘realistic’ computational models of random fields are constructed, implementations of those fields are close to continuous ones, and the conditional one-dimensional distribution in the nonempty part of the medium is quite natural. It is shown that the corresponding homogenized probability of the passage of a quantum particle is actually determined by the correlation scale and the occupancy of the medium and also by the above conditional distribution.

A data assimilation (DA) method based on the application of the diffusion stochastic process theory, particularly, of the Fokker-Planck equation, is considered. The method was introduced in the previous works; however, it is substantially modified and extended to the multivariate case in the current study. For the first time, the method is here applied to the assimilation of sea surface height anomalies (SSHA) into the Hybrid Coordinate Ocean Model (HYCOM) over the Atlantic Ocean. The impact of assimilation of SSHA is investigated and compared with the assimilation by an Ensemble Optimal Interpolation method (EnOI). The time series of the analyses produced by both assimilation methods are evaluated against the results from a free model run without assimilation. This study shows that the proposed assimilation technique has some advantages in comparison with EnOI analysis. Particularly, it is shown that it provides slightly smaller error and is computationally efficient. The method may be applied to assimilate other data such as observed sea surface temperature and vertical profiles of temperature and salinity.

The paper contains a description of the most important properties of numerical methods for solving nonlinear dispersive hydrodynamic equations and their distinctions from similar properties of finite difference schemes approximating classic dispersion-free shallow water equations.

The paper presents a new neutral atmosphere and ionosphere D region coupled general circulation model (for altitudes of 0-90 km) with a high spatial resolution. Efficient numerical methods of its implementation are developed. The properties of differential formulation for a plasma-chemical model of ionosphere D region are studied, the existence of a global attractor in the non-negative half of the phase space is proved, an efficient semi-implicit numerical scheme possessing the charge conservation law is constructed to solve the system. The problem of radio waves propagation in the ionosphere D region has been considered for the coupled model, we validated the model on the base of radio signals monitoring data and developed a computational unit for calculation of the radio signal attenuation in the lower ionosphere. A satisfactory reproduction of the D region mean state is shown and the ability to develope this model for use in applied tasks is indicated.

In the present paper we propose a new iterative method for the numerical solution of system of linear algebraic equations with symmetric positive definite and positive semidefinite matrices arising from the approximation of diffusion equations by the mixed hybrid finite element method on triangular and tetrahedral meshes. The method is based on a combination of the block steepest descent idea and nonoverlapping domain decomposition algorithm. We give the formulation of the method and a simple convergence estimate in the case of regular shaped quasiuniform meshes.

A model of asymptotically stationary piecewise-linear random processes based on homogeneous Poisson flows is considered in the paper. Exact expressions for the mathematical expectation and variance as functions of a continuous argument are presented. A model of asymptotically periodically correlated piecewise-constant non-Gaussian random processes is also presented. This model is based on inhomogeneous Poisson flows of special form.