Potential field modeling by combination of near-boundary and contact elements with non-classical finite differences in a heterogeneous medium

Abstract

In this paper, a generalized scheme for finding solutions of potential theory problems in two-dimensional piecewise-homogeneous media containing local regions with coordinate-dependent physical characteristics has been presented. To describe the additional influence of these local areas, along with the indirect methods of near-boundary and contact elements, a non-classical finite-difference method based on asymmetric finite-difference relations has been used. The software implementation of the developed approach for finding the potential of the direct current electric field in a mountain heterogeneous ridge has been carried out. Approaches to solving elliptic problems that simulate stationary processes in piecewise-homogeneous media with ideal contact conditions at the interfaces and mixed boundary conditions have been considered. They analytically take into account the condition of continuity of the unknown functions (potential, temperature) and are based on the combination of indirect methods of near-boundary and contact elements. Using the software developed, computational experiments have been carried out for the problem of exploration and forecasting of oil and gas deposits in a mountain range by the method of electrical profiling.