Modeling of Explosive Processes in Anisotropic Media where Boundary of the Influence Region is Identified


  • Andrey Bomba Rivne State Humanitarian University, Rivne, Ukraine
  • Kateryna Malash Rivne State Humanitarian University, Rivne, Ukraine



Nowadays, explosive processes are widely used for the optimization of extraction minerals processes, in the buildings construction and industry. This practice allows to significantly increase the speed of the work and, at the same time, reduce it cost. However, side effects of the explosion usage can be catastrophic, since its destructive power is capable of completely demolishing even fairly stable buildings and causing irreparable damage to the environment, therefore there is a need for a precise mathematical modeling of the explosive process with a detailed calculation of all its consequences.

One of the models used to investigate the explosion process is a fluid based on the simulation of an environment in which an explosion occurs as a filtration fluid. In this case, the velocity field generated by the explosion is usually considered to be potential.

This article deals with a mathematical model of the explosion process based on a liquid model. It takes into account the mutual influence of the deformable anisotropic porous medium parameters and the explosive process characteristics. The corresponding boundary value problem is solved using the numerical quasiconformal mappings method which ensures the possibility of its solution taking into account the presence of the reverse effect, the existence of which essentially complicates the process of solving the problem by other, less «dynamical» methods. Algorithm used in the modelling of similar processes in hydrodynamics and electrodynamics, in particular for the study of filtration processes and electromotography is adapted for solving appropriate boundary value problems. The method of identifying the external boundary of the domain of the explosive process influence is developed by introducing certain changes to the «classical» algorithm for solving such a type of boundary problems for the twice-bounded domain since the last one requires a priori assignment of the inner and outer domain contours.


Kravets V. G. Physical processes of applied geodynamics of an explosion: mon-ograph / V. G. Kravets, V. V. Korobyichuk, V. V. Boiko. — Zhytomyr : ZSTU, 2015. — 408 p.

Bulavatskii V. M.. Some inverse problems of the pulsed-hydrodynamic theory of explosion on the discharge / V. M. Bulavatskii, I. A. Luchko // Investigations on boundary value problems of hydrodynamics and thermophysics. — Kiev, 1979. — P. 53–64.

Bomba A. Ya. Nonlinear mathematical models of geohydrodynamics processes / A. Ya. Bomba, V. M. Bulavatskii, V. V. Skopetskii. — Kiiv : Naukova dumka, 2007. — 308 p.

Bomba A. Ya. Using quasi-conformal mappings to mathematical modeling of explosion processes / A. Ya. Bomba, A. M. Sinchuk // Volynskii matematychnii visnyk. Serie «Applied mathematics». — Ed. 8. — P. 32–41.

Bomba A. Ya. Modeling of the explosion process in an anisotropic medium with quasiconformal mapping methods/ A. Ya. Bomba, K. M. Malash // Transactions оf Kremenchuk Mykhailo Ostrohradskyi National University. — Kremenchuk. — 2017. Ed. 4 (105). — P. 28–33.

Bomba A. Ya. Methods of complex analysis: monograph / A. Ya. Bomba, S. S. Kashtan, D. O. Prigornytskii, S. V. Yaroshchack. — Rivne : NUWM, 2013. — 415 p.

Blair David E. Inversion theory and conformal mapping / David E. Blair. — American Mathematical Sciety, 2000. — 152 p.

Nearling James. Mathematical tools for physics / James Nearling. — Miami, 2008. — 594 p.

Prigornitskii D. O. Modification of the algorithm for numerical solving a class of nonlinear modeling boundary value problems on quasi-conformal mappings in two-coupling deformable media / D. O. Prigornitskii // Volynskii matematychnii visnyk — Serie «Applied mathematics». — Ed. 9. — 2002. — P. 60–66.

Bomba A. Ya. Numerical solution of nonlinear modeling boundary value problems on quasi-conformal mapping under conditions of interaction of gradients of potential and environmental characteristics / A. Ya. Bomba, V. V. Skopetskii, D. O. Prigornitskii // Visnyk Kiivskoho Universitetu. Serie: «Physics and math-ematics». — 2003. — Ed. 1. — P. 126–135.