Abstract
The local inertial equations, which drop the nonlinear acceleration term from the Saint-Venant equations, are effective and efficient for fast flood computation thanks to its hyperbolic nature and semi-implicit discretization of the friction term. However, mechanisms that the semi-implicit discretization works successfully has not been clarified, which is the motivation of our research. To achieve this, this study applied the von Neumann stability analysis to numerical models of the one-dimensional local inertial equations with explicit, semi-implicit, and implicit discretization of the friction term. The stability analysis led to the exact stability condition for each discretization, and reveals that the semi-implicit discretization enables much larger time step than the explicit counterpart. It was also shown that when the friction term is explicitly discretized, the maximum allowable time step has the upper limitation for coarse spatial resolution. Stability conditions obtained by a series of numerical simulations were in good agreement with the derived stability conditions. The stability analysis of this study revealed the numerical efficiency of the semi-implicit discretization of the friction term in a quantitative manner.
