Special features of difference schemes for solving the two-dimensional Navier-Stokes equations, connected with the formulation of the boundary conditions on the solid surface

Abstract

In the context of the numerical treatment of the two-dimensional Navier-Stokes equations, the boundary conditionsatasolid surface may be realized in different ways, some of which are examined. The approach considered here assumes that the equations of the system are solved separately. It is shown that then, irrespective of the specific formulation of the Navier-Stokes equations for an incompressible viscous liquid — in terms of velocity-pressure, velocity-vorticity or vorticity-stream function — the boundary conditions can be realized in an algorithmically universal way, based on a two-parameter formula previously proposed to approximate vorticity on a wall.