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3 TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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Mathematical modeling of random concentracion field and its second moments in semispace with erlangian distributions of layerd inclusions

Chernukha O., Bilushchak Y.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2016

Vol. 20, No 3

295--334

The processes of admixture diffusion in a two-phase stratified semispace with random disposition of syblayers are studied by the approach where internal random nonhomogeneities are considered as inner sources and the solution is found in the form of a Neumann series. The diffusion equations are formulated for one-connected regions of each phase and non-ideal contact conditions for the concentration on interphases are imposed. By the theory of generalized functions the contact problem is reduced to the equation of mass transfer in the whole body, which operator includes explicitly jump discontinuities of the concentration function and its derivatives. The obtained initial-boundary value problem of mass transfer is reduced to the equivalent integro-differentual equation. The solution is constructed in the form of a Neumann series and averaged over the ensemble of phase configurations with Erlangian and exponential distributions of inclusions. Dispersion and the two-point correlation function of the concentration field for diffusion are determined taking into account the probable distribution of inclusions, pair interaction of sublayers and the function of phase correlation. The dependence of the behavior of the averaged admixture concentration, field dispersion and the correlation function in the semispace with Erlangian and exponential distributions of inclusions on different medium characteristics is investigated and established.

Simulation of Diffusion Flows in Two-Phase Multilayered Stochastically Nonhomogeneous Bodies with Non-Uniform Distribution of Inclusions

Chaplya Y., Chernukha O., Davydok A.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2015

Vol. 19, No 3

321--351

Admixture diffusion flows are investigated in two-phase randomly nonhomogeneous multilayered strips with non-uniform distributions of inclusions. Cases where the most probable disposition of layered inclusions is located near the body boundary on which the mass source acts in the neighborhood of another boundary and in the middle of the body are considered. The initial-boundary value problem is formulated for the function of random mass flow under conditions of a constant flow on the upper surface and zero concentration of the admixture on the lower surface. Calculation formulae are obtained for the diffusion flow averaged over the ensemble of phase configurations in the particular cases of beta-distribution at zero and nonzero initial concentrations. The dependences of the averaged admixture flows on medium characteristics are established. It is shown that if the admixture diffusion coefficient in inclusions is greater than in the matrix, consolidation of inclusions in the middle of the body leads to an increasing diffusion flow. Simulation of the averaged diffusion flows of the admixture in the multilayered strip is performed for different model variants of a probable disposition of phases in the body and their comparative analysis is carried out.

Mathematical Modeling of Random Diffusion Flows in Two-Phase Multilayered Stochastically Nonhomogeneous Bodies

Chaplya Y., Chernukha O., Davydok A.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2015

Vol. 19, No 3

297--320

An approach for studying stochastical diffusion flows of admixture particles in bodies of multiphase randomly nonhomogeneous structures is proposed, according to which initialboundary value problems of diffusion are formulated for flow functions and methods of solution construction are adapted for the formulated problems. By this approach the admixture diffusion flow is investigated in a two-phase multilayered strip for the uniform distribution of phases under conditions of constant flow on the upper surface and zero concentration of admixture on the lower surface. An integro-differential equation equivalent to the original initial-boundary value problem is constructed. Its solution is found in terms of the Neumann series. Calculation formulae are obtained for the diffusion flow averaged over the ensemble of phase configurations under both zero and constant nonzero initial concentrations. Software is developed, a dependence of averaged diffusion flows on the medium characteristics is studied and general regularities of this process are established.