The numerical treatment of the Navier-Stokes equations

The numerical calculation of the approximate solutions for flow velocity and pressure of the Navier-Stokes equations describing the time evolution of a viscous flow are treated. A method for the construction of approximate solutions for the equations in the case of conservative external forces (F=0) was developed. It allows to approximate equations using so-called particle methods; the solutions have a high degree of regularity; convergence predictions are demonstrated. A difference method, based on the Rothe method which takes into account external forces (F not = 0) and a general three-dimensional flow was developed. Approximation theory, stability and convergence analysis, and numerical tests are presented. Examples for which the exact solutions are known were calculated showing agreement within 2% with the exact solutions.