A perfectly matched layer formulation for the nonlinear shallow water equation models: The split equation approach

I. M. Navon, B. Neta, M. Y. Hussaini

We consider the development of the PML equations for the two dimensional linearized shallow-water equations. The method uses the splitting technique, i.e. the absorbing layer equations are obtained by splitting the governing equations in the coordinate directions and absorbing coefficients are introduced in each split equation.

The method is tested on the nonlinear shallow-water equations including the Coriolis factor on a limited-area domain for a convective mean flow. The numerical results indicate that outgoing waves are leaving the domain without perturbing the flow in the physical domain. No filters were used in the numerical experiments which included both a stationary as well as a convected Gaussian. The exterior domain was ended using characteristic well posed boundary conditions for the shallow water equations.The error computed using only characteristic boundary conditions as well as the second order Engquist and Majda boundary conditions was used for comparison purposes. The efficacy of the PML scheme for the nolinear shallow water equations was confirmed . PML layers of increasing thickness yielded better results than the characteristic treatment.