Variational method for solving the boundary value problem of hydrodynamics

Abstract

Abstract The analysis of the application of the variational method for solving the boundary value problem of hydrodynamics is carried out. From the point of view of numerical research of mathematical physics problems, these variation formulations are considered as the basis of projection methods (the Ritz method). The article presents the main techniques that allow reducing the cost of machine time and speed up the convergence of the computational process when calculating the hydrodynamic characteristics of cavities of various configurations. Using the Trefts method allows you to reduce the calculation time of the boundary value problem. The green transformation allows us to reduce the three dimensional integral to a one-dimensional. This creates a universal method for determining hydrodynamic coefficients for rotation cavities with an arbitrary contour of the Meridian section. However, for most configurations of cavities, the convergence rate is satisfactory and provides numerical values with a high degree of accuracy.