The stability of boundary conditions in the numerical solution of the time-dependent Navier-Stokes equations

Abstract

This paper investigates the stability of finite-difference schemes, including boundary conditions, for solving the time-dependent Navier-Stokes equations. The different types of boundary condition whioh may occur are listed and no-slip conditions are derived for a wall with suction. Stability analyses are completed for one-dimensional problems with various types of boundary conditions, using schemes suitable for two-dimensional problems. All the conditions introduced are shown to be stable if there is no flow across the boundary. For suction at a fixed or moving wall, it is shown that the mesh size must be restricted for both accuracy and stability.