Numerical stability analysis of the local inertial equation with semi- and fully implicit friction term treatments: assessment of the maximum allowable time step

抄録

The local inertial equation (LIE) as a simple mathematical model has been widely used for flood simulation. So far, the maximum allowable time step of the discretized LIE with the conventional semi-implicit scheme has been believed to follow the standard Courant-Friedrichs-Lewy condition. However, we demonstrate that this is not true from the viewpoint of a numerical stability analysis considering the model non-linearity. In addition, a fully-implicit variant of the scheme with higher stability is presented, indicating its practical advantages.