<p>The work is devoted to numerical simulation of the problems of flowing around moving bodies. The main equations of heat and mass transfer of a viscous compressible gas are provided. To describe the flow over the object with moving boundaries, a motion velocity vector is introduced into the numerical scheme of the finite-volume method. The computation method on meshes with overlapping (or overset grids) was considered as a simulation approach. Key stages of the proposed computation technology are given. To reduce the computational complexity of generating an interpolation stencil, the use of hierarchical data structures is proposed. Reconstruction methods described in the work are based both on well-known algorithms for interpolating computed values, and original methods based on the use of gradients of computation fields and on the use of a four-point stencil. To demonstrate the operability of the algorithms, the problem of subsonic flow around the two-link airfoil section and the task of separating the store from the wing with the pylon in the transonic flow of a compressed gas are considered. The primary objective of this work is to develop an efficient numerical model based on unstructured overset grids for solving applied problems of fluid-moving body interaction in the interests of the aviation industry. The analysis of the obtained results for the separation problem has shown the advantage of the proposed reconstruction approaches with respect to standard interpolation methods, which made it possible to increase the accuracy of prediction of aviation angle dynamics by more than 15% at the final simulation interval.</p>