On one class of difference schemes for solution of Navier-Stokes equations in velocity-pressure variables

Abstract

Difference methods in velocity-pressure variables having a number of important properties are constructed and investigated in this paper for a two-dimensional Navier-Stokes equation. Power neutral approximations of convective members and pressure gradients ensure a conservativity and absolute stability of the proposed algorithms. Their stability and convergence are investigated. The existence and uniqueness of velocity components and pressure gradients is proved.