Stability Analysis of Two‐Dimensional Depth‐Averaged Model

Abstract

An analysis of numerical stability of a two‐dimensional depth‐averaged hydrodynamic model is made by examining the linearized finite difference governing equations based on Fourier analysis. The eigenvalues of the amplification matrix are solved by an iteration technique. They are used to check the derived theoretical stability criterion that has an exponential form. Two case studies are considered, one dealing with a small channel with a sidepool and the other dealing with the large shallow Songkhla Lagoon. The results obtained by the stability analysis and by running the hydrodynamic model are found to agree closely for the case of the small channel. From these results, an equivalent empirical stability criterion similar to the Courant condition is established for practical purposes.