**1. Introduction**

For the mathematical simulation of thermal field distribution in the ground, it is necessary to account for convective heat transfer (heat transfer by means of mass transfer). Convective heat transfer is caused by the filtration of water into the ground resulting, for example, from precipitation. The temperature distribution is described by the partial differential equation of heat conduction where, in the case of convection, there is a so-called convective term. Since the computational domain is arbitrary, the heat equation is solved numerically by using finite-difference methods (FDM). The Douglas – Rachford ADI scheme is one of these methods. In this paper, we focus on modification of the scheme to account for convection in the computational domain.