Volume 40, Issue 1

A technology for numerical analysis of the local biglobal stability of laminar incompressible boundary layers over streamwise-ribbed surfaces is proposed. Within its framework, the stability is studied using the locally-parallel approximation and Floquet theory. The work of the proposed technology is demonstrated by the example of a boundary layer over a streamwise-ribbed plate of finite thickness. For the considered values of ribbing parameters, it is shown that the presence of ribbing increases the growth of disturbances compared to a plate without ribbing, thereby promoting the natural laminar–turbulent transition.

Two approaches to the problem of statistical separation of finite mixtures of probability distributions are discussed. The first of them consists in finding maximum likelihood estimates of the parameters of the mixture by the EM-algorithm, whereas the second approach consists in finding the values of the parameters that deliver minimum to the distance between the theoretical and empirical distribution functions. It is demonstrated that the second approach is preferable at least in the problem of statistical reconstruction of the coefficients of an Itô stochastic process that requires dynamic separation of finite normal mixtures in the moving window mode. For this problem, the performance of the numerical procedures is critical. A combination of numerical procedures is described that provides (almost) the same value of the likelihood function for the second approach that is attained by the EM-algorithm, but ensures multiple decrease of the ℓ 2 -distance between the theoretical mixture and the empirical distribution function while demonstrating better performance. A kind of ‘metric’ regularization of the problem of likelihood maximization is proposed. The proposed techniques are illustrated by adjusting the Itô process model to the time series of the interplanetary magnetic field (magnetic flux density) registered by the Global Geospace Science (GGS) Wind apparatus (the spacecraft placed in the Lagrange point between the Earth and the Sun).

This paper presents the developed four-dimensional variational data assimilation system for the global ionosphere model INM-IM. The first results on realistic observational total electron content data assimilation are shown. The formulation of the problem is given, numerical methods for solving the system of direct and adjoint equations are proposed. The results of preliminary numerical experiments with developed assimilation system for the unperturbed ionospheric conditions are also presented, a comparison of obtained results in vertical electron content distribution with observed diurnal evolution is given.

The paper demonstrates constructing monotone difference scheme for the two-dimensional (in space) transfer equation in divergent form by the Lagrangian–Eulerian approach. It is based on the use of spatial grids formed by the approximate traces of the characteristics for this operator. The use of such special grids made it possible to circumvent the limitation by S. K. Godunov on the absence of monotone schemes above the first order of convergence. A brief theoretical justification for the second order of convergence and supporting results of the computational experiment are presented.

In this paper, we apply low rank approximations to a large dense matrix in the solution of an integral equation in the problems of electromagnetic wave diffraction on a perfectly conductive object. In the case of a large wave number, the matrix of the system becomes ill-conditioned, therefore, we propose to use a preconditioner to solve the system with such a matrix by an iterative method. Based on block-sparse matrices, two types of preconditioners are constructed in this paper. Low-rank approximations are used to store the factors of the LU decomposition of the preconditioner matrix. The preconditioners make it possible to obtain a solution to the diffraction problem on a perfectly conductive object of 120 wavelengths.

We deal with an initial-boundary value problem for the multidimensional acoustic wave equation, with the variable speed of sound. For a three-level semi-explicit in time higher-order vector compact scheme, we prove conditional stability and derive 4th-order error bound in the enlarged energy norm. It exploits additional sought functions which approximate 2nd-order non-mixed spatial derivatives of the exact solution. At the first time level, a similar two-level in time scheme is applied, without using derivatives of the data in the problem. No iterations are required to implement the scheme. We also present results of various 3D numerical experiments. They demonstrate a very high accuracy of the scheme, for smooth data, and its advantages in the error behavior over the classical explicit 2nd-order scheme, for nonsmooth data. An example of the wave in a layered medium (with a discontinuous speed of sound) initiated by the Ricker-type wavelet source function is also included.