Leshchuk O. Determination of dynamical characteristics of bounded volume of viscous fluid by projection method

Projection method for solving the problem about eigenvibration of viscous incompressible fluid with free surface in stationary vessel is presented. For cylindrical and hemispherical vessels by means of hydrodynamical representations coordinate functions were built. These functions satisfy the equations of motion into a region and a part of boundary conditions. Numerical realization of the projection method for these types of vessels with and without surface tension was held. Computed values of damping rates and eigenfrequencies define more precisely calculations of previous authors and are found to be in good agreement with experimental data. A technique for determination of main vector and main moment of hydrodynamical forces which act on the vessel are described. For some specified vessels a type of singularities of solutions in corner points for two-dimensional problem with viscous fluid and for spatial problem with ideal fluid are investigated. The coordinate functions which repeat these singularities are built. It is shown that the application of these special coordinate functions allows to increase greatly a precision of desired solution as compared with situation if we use only smooth coordinate functions.