On boundary conditions and numerical methods for the unsteady incompressible Navier–Stokes equations

Abstract

Numerical methods and boundary conditions to solve the unsteady incompressible Navier–Stokes equations are discussed. It is shown, via the analysis of the governing partial differential equations and their discretized algebraic equations, that boundary conditions necessary to solve the incompressible Navier–Stokes equations are conditions either for the normal and tangential components of velocities or alternatively for the normal velocity and tangential vorticity components. In an explicit formulation, the solution of the resulting system of algebraic equations is got more efficiently by solving either the pressure or velocity Poisson equation. The boundary conditions necessary to solve these Poisson equations are provided from velocity boundary conditions and momentum equations. Results of numerical simulations of some selected unsteady flows are also presented.