Time-step Criteria and Fourier (von Neumann) Stability Analysis of Two-Dimensional Finite Element Schemes for Shallow Water Equations

Abstract

This paper presents a stability-based analysis of amplification factors obtained usingFourier or von-Neumann method for the finite element formulation of shallow water equations. AGalerkin finite element model is developed for two-dimensional shallow water equations to obtainlinearized form of the error equations. Fourier analysis is performed at finite element and node levelsto propose time-step criteria for consistent methods using explicit, semi-implicit, and implicitschemes. The amplitude behavior as a function of the Courant and wave numbers is analyzed forsquare elements for two-dimensional field solution at each computational grid node.