Home – Home – Jornals – Numerical Analysis and Applications 2014 number 3

A cellular automata model of population dynamics of three organisms in Lake Baikal is proposed and investigated. Each species is divided into age groups. There are eight groups all together. The model allows one to take into account a spatial organisms distribution, a seasonal dependency of birth rates, a possible habitat pollution and water streams. A computational experiment was carried out for the case of pollution that is in the south area of lake Baikal. It demonstrates that the population dynamics tends to the oscillating process with a period equal to 1 year. The assessment of the critical pollution intensity which leads to the total extinction is presented. The model was verified within production-to-biomass and frequency of occurrence ratios.

The gas flows in the gravity field through the porous objects with energy sources, which may originate from the natural or man-caused disasters, have been investigated. An OpenMP version of the parallel algorithm has been developed for the calculation of unsteady 2D gas flows through porous self-heating media of complex subsurface geometries. The structure of the sequential algorithm and the transition from it to the OpenMP version have been described, the performance and efficiency of parallelization have been analyzed. The unsteady gas flows through axisymmetric porous self-heating objects with a partial closure of the object outlet (with a top cover) have been investigated by means of the developed parallel algorithm. The influence of the partial closure of the object outlet on the cooling process of the porous objects with a non-uniform distribution of heat sources has been analyzed.

The generation method of quadratic-linear bilevel optimization test problems in a pessimistic formulation is proposed and justified. The propositions about the exact form and the number of local and global pessimistic solutions in generated problems are proved.

A high-accuracy Runge-Kutta/WENO method up to fourth order with respect to time and fifth order with respect to space is developed for the numerical modeling of the small-amplitude wave propagation in a steady fluid-saturated porous medium. The system of governing equations is derived from the general thermodynamically compatible model of a compressible fluid flow through a saturated elastic porous medium, which is described by the hyperbolic system of conservation laws with allowance for finite deformations of the medium. The results of numerical solution of one- and two-dimensional wavefields demonstrate efficiency of the method developed.

We study the convergence of an H ¹-Galerkin mixed finite element method for parabolic problems in one space dimension. Both semi-discrete and fully discrete schemes are analyzed assuming reduced regularity of the initial data. More precisely, for a spatially discrete scheme error estimates of order \mathcal{O}( h ² t ^-1/2) for positive time are established assuming the initial function p ₀ ϶ H ²(Ω) ∩ H ₀ ¹(Ω). Further, we use an energy technique together with a parabolic duality argument to derive error estimates of order \mathcal{O}( h ² t ^-1) when p ₀ is only in H ₀ ¹(Ω). A discrete-in-time backward Euler method is analyzed and almost optimal order error bounds are established.

For interval matrices, the paper considers the problem of determining whether a matrix has a full rank. We propose the full rank criterion that relies on the search for diagonal dominance as well as criteria based on pseudoinversion of the midpoint matrix and comparison of the midpoint and the radius matrices for the interval matrix under study.

A numerical model for studying the dynamic mixing of the sea and the river waters in the estuarial area is proposed. Computations are based on the two-dimensional longitudinal vertical stratified fluid mechanics equations and the equation of transport of salt. The model focuses on the reproduction of the local density currents at the mouth of arms branched deltas of the rivers of Siberia. The results of numerical experiments are given, the dynamic structure of the flow and salinity profiles are compared to the observational data.