Identification of coordinates of impulse sources of wastewater pollution in piecewise homogenous media using Numerical Quasiconformal Mapping Methods

The process of filtration in a single-connected curvilinear domain bounded by streamlines and equipotential lines is considered, provided that the medium under study is piecewise homogeneous. It is assumed that certain unknown curves act as impulse sources of pollution. It is assumed that their propagation occurs only due to the convective component, without significantly affecting the filtration background. It is proposed to use the method of characteristics for solving the convection equation to identify the coordinates of pollution sources. In this case, quasipotentials at the fluid inlet and outlet at the boundary of the domain, coordinates of the points of pollution detection, and the time of its movement downstream can serve as a priori data. The general algorithm involves the adaptation of the numerical quasiconformal mapping method to build a hydrodynamic mesh, according to which the coordinates of pollution sources are identified. Numerical experiments were carried out and analysed. In particular, it is emphasised that with a sufficient mesh division, the maximum discrepancies between the a priori known data and the calculated data are small compared to the size of the studied domain. This indicates the effectiveness of the developed algorithm for identifying pollution sources in the case of a piecewise homogeneous environment. As an additional measure to reduce the magnitude of the uncertainties, it is proposed to use more accurate approximation schemes for specific expressions. On the other hand, there is an increase in computational complexity compared to the case of a continuous setting of the filtration coefficient. Given the relatively high accuracy of the calculations, it seems advisable to further develop an described approach to larger-scale in comparison with point sources of pollution and to spatial case. Taking into account the sensitivity of the solutions to the discontinuity of the filtration coefficient values, it is also worthwhile to introduce additional conditions at the contact of homogeneous media in the future.