Numerical approximation of viscous terms in finite volume models for shallow waters

Two methods for the numerical treatment of viscous terms in shallow water equations are studied and computational details are given for structured grids. It is demonstrated that the first scheme, which is widely used, may lead to spurious oscillations arising from computational modes. In fact, the shortest resolvable waves of wave length 2Δx are invisible to this method. The second method, although more expensive, is free of computational modes and it presents a more accurate approximation of viscous terms. The dispersion relation of the second method is closer to the analytical case and it has a smaller truncation error, which is due to the fact that it uses a more localized control volume. Numerical experiments are also presented that support the study. Copyright © 2009 John Wiley & Sons, Ltd.