ON BOUNDARY-CONDITIONS FOR UNBOUNDED FLOWS

We examine a method to impose boundary conditions on arbitrary boundaries, introduced to make domains of infinite extent finite for the purpose of numerical calculations, when a finite element discretization based on linear, bilinear or trilinear elements is used, in one, two or three dimensions, respectively. In I particular, we look at the so-called 'free' boundary condition, which consists in retaining the boundary integrals generated by the weighted-residuals formulation along the open boundaries and adding them to : the stiffness matrix. We show that this procedure is exactly equivalent to imposing on the boundary nodes a :Sommerfeld radiation condition in one dimension, and a slightly modified form of the Sommerfeld boundary condition in two and three dimensions. We also show that the procedure is not applicable to the purely elliptic case.