An analytical numerical method for the construction of solutions to boundary-value problems for the two-dimensional stationary Navier–Stokes system using complex analysis techniques

A new method is examined for the construction of approximate solutions to boundary value problems for the Navier–Stokes equations, which describe plane stationary flows of a viscous incompressible fluid. The method is based on the use of the complex form of the original equations and on the representation of the unknown complex-valued functions and the corresponding conjugate functions by their expansions in powers of the conjugate independent variable, the coefficients being holomorphic functions. A method of partitioning into analytic elements with subsequent sewing is proposed. The use of this method makes it possible to construct approximate solutions in domains with a fairly complicated configuration. As an illustration, the numerical results are given for the flow in a canal with a notch.