Fourier Analysis of Dissipative fem Channel Flow Model

Abstract

The algorithmic properties of a dissipative Galerkin scheme for openchannel flow are investigated by means of a Fourier analysis based on the linearized equations describing kinematic and dynamic wave motion in shallow water. Optimum dissipation levels are determined so that the kinematic wave speed error is reduced by two orders of magnitude compared to that of the standard Galerkin method. The method is then extended to the equations of dynamic‐wave propagation written in conservation form and the dissipation and phase characteristics of the scheme are determined and compared to the corresponding properties of some well‐known finite‐difference schemes. The dissipative Galerkin scheme exhibits some remarkable characteristics, which include unconditional stability, a highly selective dissipative interface and very satisfactory wave‐speed characteristics. The overall wave deformation characteristics of the method are found to be not only an improvement of the classical Galerkin method but also better than some of the most popular finite‐difference methods used widely in unsteady open‐channel flow.