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

Abstract

A limited-area model of nonlinear shallow water equations (SWE) with the Coriolis term in a rectangular domain is considered. The rectangular domain is extended to include the so-called perfectly matched layer (PML). Following the proponent of the original method, the PML equations are obtained by splitting the shallow water equations in the coordinate directions and introducing the damping terms. The efficacy of the PML boundary treatment is demonstrated in the case where a Gaussian pulse is initially introduced at the center of the rectangular physical domain. A systematic study is carried out for different mean convection speeds, and various values of the PML width and the damping coefficients. For the purpose of comparison, a reference solution is obtained on a fine grid on the extended domain with the characteristic boundary conditions. The L2 difference in the height field between the solution with the PML boundary treatment and the reference solution along a line at a downstream position in the interior domain is computed. The PML boundary treatment is found to yield better accuracy compared with both the characterisitic boundary conditions and the Engquist-Majda absorbing boundary conditions on an identical grid.