Application of Kufarev method to problem of subsoil waters movement under hydraulic engineering constructions

S. Jambaa ; T. V. Kasatkina ; A. M. Bubenchikov

Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 47 (2017), pp. 15-21

Résumé

To solve plane filtration problems that are described by the classical Darcy motion law, it is proposed to apply the method of conformal mappings implemented in the form of Kufarev’s approach. This approach makes it convenient to find the constants entering into the Schwarz–Christoffel integral as the result of solving a system of ordinary differential equations. The system of differential equations for $b_k=a_k-\lambda$ (here $a_k$ are the prototypes of the polygon vertices, $\lambda$ is the prototype of the cut vertex) is solved with the use of matrix technologies in the MatLab system. In this case, the solution of the problem of constructing groundwater streamlines and lines of constant pressure is reduced to computing the matrix on a discrete set of its arguments and displaying the rows or columns of this matrix. Using the described solution construction technique, the motion of groundwater under a dam with a specific geometrical shape and depth in the ground at the existing difference between flood levels before and after the dam is considered.

Détail

Keywords: conformal mapping of rectilinear polygons, prototypes of polygon vertices, streamlines and lines of constant pressure.