Discrete transparent boundary conditions for the two-dimensional leap-frog scheme: approximation and fast implementation

We develop a general strategy in order to implement approximate discrete transparent boundary conditions for finite difference approximations of the two-dimensional transport equation. The computational domain is rectangle equipped with Cartesian grid. For leap-frog scheme, we explain why our provides explicit numerical on four sides and it does not require prescribing any condition at corners domain. stability each side analyzed by means so-called normal mode analysis. Numerical investigations full problem show that strong instabilities may occur when coupling stable strategies rectangle. Other yield promising results.