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Numerical Analysis and Applications

2014 year, number 3

A cellular automata model of three organisms populations in lake Baikal

I.V. Afanasyev
Institute of Computational Mathematics and Mathematical Geophysics SB RAS, pr. Lavrentjeva, 6, Novosibirsk, Russia, 630090
Keywords: клеточный автомат, дискретное моделирование, динамика численности, Байкал, хищник-жертва, cellular automata, discrete modeling, populations dynamics, lake Baikal, prey-predator systems

Abstract >>
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.

An OpenMP version of the parallel algorithm for calculation of unsteady gas flow through porous objects with energy sources: Analysis and Application

N.A. Lutsenko1,2, G.V. Tarasov1,2, K.A. Gyrnik2
1Institute of Automation and Control Processes, 5 Radio St., Vladivostok, 690041, Russia
2Far Eastern Federal University, Suhanova st. 8, Vladivostok, , 690050, Russia
Keywords: параллельные алгоритмы, численное моделирование, пористые среды, газовое охлаждение, тепловыделение, parallel algorithms, numerical modeling, porous objects, gas cooling, heat release

Abstract >>
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 test problem generation for quadratic-linear pessimistic bilevel optimization

A.V. Orlov1, A.V. Malyshev2
1Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences, Lermontov str., 134, 664033, Irkutsk, Russia
2Luxand, Inc., 901 N. Pitt str. Suite 325 Alexandria, VA 22314 USA
Keywords: генерация тестовых задач, двухуровневая оптимизация, гарантированное (пессимистическое) решение, задачи-ядра, test problem generation, bilevel optimization, guaranteed (pessimistic) solution, kernel problems

Abstract >>
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.

The Runge-Kutta/WENO method for solving equations for small-amplitude wave propagation in a saturated porous medium

A.S. Romankov1, E.I. Romenski2
1Novosibirsk State University, Pirogova 2, 630090, Novosibirsk, Russia
2Sobolev Institute Mathematics of SB RAS, 4 Acad. Koptyug avenue, 630090, Novosibirsk, Russia
Keywords: методы высокого порядка точности, гиперболические системы законов сохранения, насыщенные пористые упругие среды, распространение волн, high-accuracy methods, hyperbolic system of conservation laws, saturated elastic porous media, wave propagation

Abstract >>
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.

Convergence of H 1-Galerkin mixed finite element method for parabolic problems with reduced regularity of initial datas

M. Tripathy, Rajen Kumar Sinha
Indian Institute of Technology Guwahati, Guwahati, 781039, India
Keywords: параболические задачи, H -смешанный метод конечных элементов Галеркина, полудискретная схема, обратный метод Эйлера, оценки ошибки, parabolic problems, H -Galerkin mixed finite element method, semi-discrete scheme, backward Euler method, error estimates

Abstract >>
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.

On the full rank interval matrices

S.P. Shary
Institute of computationatl technologies SB RAS, pr. Lavrentjeva, 6, 630090, Novosibirsk, Russia
Keywords: интервальная матрица, полный ранг, признак полноранговости, interval matrix, full rank, full rank criteria

Abstract >>
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 of density currents in estuaries of the Siberian rivers

V.A. Shlychkov1, A.I. Krylova2,3
1Institute for Water and Environmental Problems, 630090, Novosibirsk, Russia
2Institute of Computational Mathematics and Mathematical Geophysics SB RAS, pr. Lavrentjeva, 6, 630090, Novosibirsk, Russia
3Novosibirsk State University, Pirogova 2, 630090, Novosibirsk, Russia
Keywords: численное моделирование, турбулентность, градиентно-плотностные течения, речной поток, морская акватория, перенос соли, numerical simulation, turbulence, gradient-density flows, river flow, sea area, transport of salt

Abstract >>
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.