Artificial boundary conditions for incompressible Navier–Stokes equations: A well-posed result

Abstract

Numerical simulation of two-dimensional incompressible viscous flows around an obstacle is considered. 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 and a series of approximate artificial boundary conditions on them are derived by imposing the continuity of velocity and the normal stress. Thus the original problem is reduced to a problem defined in a bounded computational domain. The well-posedness of the reduced problem is proved. The finite element approximation of this problem is given and error estimates are obtained. Furthermore numerical examples show the accuracy and efficiency of our artificial boundary conditions.