Numerical analysis of open boundary conditions for incompressible viscous flow past a square cylinder

The issue of open, or outflow, boundary conditions is important in the numerical simulation of incompressible viscous flows. However, there are few studies of this problem because it is very difficult to give exact mathematical conditions for finite and artificial boundaries. In this paper, four types of open boundary conditions are compared numerically in a two-dimensional flow past a square cylinder using a finite difference method. They are a free outflow condition and three kinds of Sommerfeld radiation conditions based on the free stream velocity at infinity, Halpern's analysis, and the local velocity. The free outflow condition deforms velocity and pressure fields, while the Sommerfeld radiation condition utilizing the free stream velocity has the least influence on the flow.