Identification of Coordinates of Impulse Sources Using Numerical Quasiconformal Mapping Methods

Abstract

The process of convective transfer of substances during filtration in a po-rous medium (horizontal layer) is considered. An approach to determining the coordinates and action time of a special typeof 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, infor-mation about the trajectories (which coincide with the flow lines)of the movement of the impurity substance and the time intervals of the flow of pol-lution 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 ahydrodynamic motion mesh). Its solution is based on the procedure of quasiconformal map-ping 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 char-acteristic 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 fur-ther transfer to more complex cases of fluid motion,in particular, with addi-tional consideration of the diffusion component, generalization to space, etc.