The global artificial boundary conditions for numerical simulations of the flow around a submerged body

We consider the numerical approximations of the two-dimensional steady potential flow around a body moving in a liquid of finite-constant depth at constant speed and distance below a free surface. One vertical segment is introduced as the upstream artificial boundary and two vertical segments are introduced as the downstream artificial boundaries. On the artificial boundaries, a sequence of high-order global artificial boundary conditions are given. Then, the original problem is reduced to a problem defined on a finite-computational domain, which is equivalent to a variational problem. After solving the variational problem by the finite-element method, we obtain the numerical approximation of the original problem. The numerical examples show that the artificial boundary conditions given in this paper are very effective.