Abstract
This paper discusses a method for constructing orthogonal curvilinear grids in a domain with complex geometry. The objective is to present an algorithm for numerical grid generation that allows one to efficiently and accurately solve equations of mathematical physics. The upper boundary is described by the hyperbolic tangent function, and its derivative is used to calculate the arc length. Based on the obtained metric coefficients, difference schemes are constructed in the first and second directions, and the coordinates x1 and x2 are calculated using the tracking method. The calculation process is controlled by the stability condition and stops at a given accuracy. In addition, the parabolic continuation method is used to refine the grid. The proposed method provides an accurate and stable grid structure in domains of complex shape, which allows one to accurately model the processes of flow, heat and mass transfer. In the calculations, the SymPy library of the Python 3.9 programming language was used. Using the methods of symbolic integration and differentiation, analytical forms of equations are obtained, which increases the accuracy of calculations.