High-order one-way model nesting in dispersive non-uniform media

Global–regional model interaction is considered for two-dimensional linear time dependent waves in a dispersive non-uniform medium with a continuously varying wave speed. The setup, which is sometimes called ‘one-way nesting,’ arises in Numerical Weather Prediction (NWP) as well as in other fields concerning waves in very large domains. The Carpenter scheme for this type of problem is revisited, in the context of the dispersive wave equation with a variable wave speed. The original Carpenter scheme is based on the Sommerfeld radiation operator, and thus is associated with low-order accuracy. By replacing the Sommerfeld operator with the high-order Hagstrom–Warburton absorbing operator, a modified Carpenter open boundary condition emerges which possesses high-order accuracy. This is demonstrated via a numerical example in a wave guide with a wave speed which varies linearly in the cross section.