Ідентифікація координат імпульсних джерел числовими методами квазіконформних відображень

• Дата: 2022
• Автори: Бомба, Андрій, Бойчура, Михайло, Багнюк, Ольга, Абдулалі, Амхемед
• Формат: Стаття
• Мова: Ukrainian
• Опубліковано: Kamianets-Podilskyi National Ivan Ohiienko University 2022
• Онлайн доступ: http://mcm-tech.kpnu.edu.ua/article/view/269324
• Назва журналу: Mathematical and computer modelling. Series: Technical sciences

The process of convective transfer of substances during filtration in a porous medium (horizontal layer) is considered. An approach to determining the coordinates and action time of a special type of impulse sources (pollution, heat, explosion, etc.) is proposed, based on the assumption that the latter have no significant effect on the filtration background. For identification, information about the trajectories (which coincide with the flow lines) of the movement of the impurity substance and the time intervals of the flow of pollution from their sources to the corresponding places (points) of observation (detection) is used. It is proposed to identify the coordinates of point sources using characteristic (in relation to the convection equation) functions, a priori information about the movement of pollution, and given coordinates of the nodes of the constructed hydrodynamic mesh. Significant simplifications for the process of constructing the solving algorithm are achieved by replacing the existing model problem of finding the functions of the quasipotential and the flow in complex by the corresponding inverse problem (which, among other things, provides the possibility of effectively constructing a hydrodynamic motion mesh). Its solution is based on the procedure of quasiconformal mapping of the corresponding quadrangular complex quasipotential domain into a given physical domain. Numerical experiments are presented and analyzed. In particular, it was found that the accuracy of identification of pollution sources depends significantly on the available values of quasiconformity residuals. Their greatest values are achieved on those flow lines that pass through characteristic points (so-called «key points») or near stagnant zones. It is possible to reduce the errors generated by the latter, in particular, with a large number of partition nodes. The developed algorithm provides opportunities for its further transfer to more complex cases of fluid motion, in particular, with additional consideration of the diffusion component, generalization to space, etc.