Simple and efficient solution of the shallow water equations with source terms

A simple and efficient method to solve the one-dimensional shallow water equations with source terms is presented. To avoid a fractional step method for the discretization of the source terms, a homogeneous form of the shallow water equations is proposed and well-known conservative numerical schemes are modified to solve the new form of the equations. The modification to the homogeneous form equations combines the source terms with the flux term and solves them by the same solution structure of the numerical scheme. As a result, the source terms are automatically discretized to achieve perfect balance with flux terms without any special treatment and the method does not introduce numerical errors. The proposed method is verified against several benchmark tests and shows good agreement with analytical solutions.