This article presents a numerical approach for constructing an adaptive grid in a domain with complex geometry, based on the equivalent distribution method. A control function was applied in adaptive grid generation, enabling accurate regulation of grid density in geometrically complex regions. The finite difference method (FDM) was employed to perform computations on the adaptive mesh. Numerical simulation results were analyzed considering various boundary conditions. The calculations were implemented using the Python 3.9 programming language and the SymPy library. Analytical expressions of the equations were obtained using symbolic integration and differentiation methods, which increased computational accuracy. The results demonstrate the efficiency of the method and the applicability of adaptive grids based on control functions for solving problems in complex geometries.