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

2 2015

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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.