Poisson bracket and integrals of motion in the problem of viscous fluid flow around an arbitrary flat contour

Abstract

The Poisson bracket is used to find the integrals of motion. A numerical and analytical method is suggested to solve Navier-Stokes equations in Helmholtz form. The approximation of the sought solution by a linear combination of basis functions lies in this method’s core. The main idea behind this method is to select basis functions and generalized independent variables. A functional series is taken as the required solution, found from the equation’s solution obtained by equating the Poisson bracket to zero. The substitution of the selected solution into the Helmholtz equation reduces it to a nonlinear algebraic system. This system is solved analytically for a range of cases due to its structure. The authors present an algorithm for solving the boundary problem of viscous incompressible fluid flow around an arbitrary flat contour. In laminar flow around the body, the geometric dimension decreases, and the boundary problem is reduced to a linear system of algebraic equations. The solutions were tested on solving viscous fluid flow around a wedge and a thin plate.