Artificial boundary conditions for two-dimensional incompressible viscous flows around an obstacle

In this paper we consider numerical simulation of incompressible viscous flow around an obstacle in velocity-pressure formulation. Two horizontal straight line artificial boundaries are introduced and the original flow is approximated by a flow in an infinite channel with slip boundary condition on the wall. Then two vertical segment artificial boundaries are introduced to limit the channel to a bounded computational domain. In the region of the channel between the vertical boundaries and infinity, the velocity of the flow is almost a constant vector, in which the Navier-Stokes equations can be linearised by Oseen equations and thus a general solution can be derived by using separation of variables. Artificial boundary conditions on the vertical segments are then designed by imposing the continuity of velocity and normal stress. Therefore, the original problem is reduced to a boundary value problem on a bounded computational domain. Numerical example shows that our artificial boundary conditions are very effective.