Volume 30, Issue 4

A mathematical model of the dynamics of the Baltic Sea is considered. A problem of variational assimilation of sea surface temperature (SST) data is formulated and studied. Based on variational assimilation of satellite observation data, an algorithm solving the inverse problem of heat flux restoration on the interface of two media is proposed. The results of numerical experiments reconstructing the heat flux functions in the problem of variational assimilation of SST observation data are presented. The influence of SST assimilation on other hydrodynamic parameters of the model is considered.

The stability problem for spatial structure of plasma oscillations in the process of their dynamics is studied in the paper analytically (by perturbation methods) and numerically. It is shown that if the initial perturbation possesses a local symmetry, then an overturn of oscillations appears simultaneously on a circumference of some nonzero radius. If cross-sections of the initial perturbation of the electron density are ellipses, then a singularity of the electron density appears simultaneously too, but only at two spatial points. The results of calculations performed in the Supercomputing Center ‘Chebyshev’ of Lomonosov Moscow State University using a hybrid parallel code are presented. The results are in a good agreement with analytic calculations and computations with one-dimensional models.

Numerical technique for studying surface waves appearing under the motion of a submarine landslide is discussed. This technique is based on the application of the model of a quasi-deformable landslide and two shallow water models, namely, the classic (dispersion free) one and the completely nonlinear dispersive model of the second hydrodynamic approximation. Numerical simulation of surface waves generated by a large model landslide on the continental slope of the Black Sea near the Russian coast is performed. It is shown that the dispersion has a significant impact on the picture of propagation of tsunami waves on sufficiently long paths.

This paper elaborates a new approach to nonlinear filtering based on an accurate implementation of the continuous-discrete extended Kalman filter. It implies that the moment differential equations for calculating the predicted state mean of stochastic dynamic system and the corresponding error covariance matrix are solved accurately, i.e. with negligible error. The latter allows the total error of the extended Kalman filter to be reduced significantly and results in a new Accurate Continuous-Discrete Extended Kalman Filtering method. The developed technique is compared theoretically and numerically with other implementations of the extended Kalman filter to conform its outstanding performance on test examples.

Algorithms for stochastic simulation of spatial-temporal CCD LIDAR returns are presented in the paper. Conditions for a laser pulse to generate an expanding ring of light in a cloud layer are studied by Monte Carlo numerical experiments. The algorithms developed here are aimed to supercomputer simulation.