A high resolution finite volume model for 1D debris flow

• A high-resolution numerical model is developed for resolving 1D debris flow in the non-erodible channel.
• The model is incorporated with a novel implicit treatment for friction term and a new CFL condition.
• The model is tested by comparing its solutions with analytical solutions and by applying it to two debris flows experimentally investigated in laboratory flumes.

A high-resolution (HR) numerical model for solving 1D shallow water equations employing Voellmy flow resistance relation is developed to predict the time-dependent behavior of non-Newtonian debris flow dynamics in non-erodible channel. The governing equations are solved by the HR shock-capturing method employing the HLLC approximate Riemann solver and the TVD limiter. Based on the fractional-step approach, source terms are treated by an implicit method which makes the model well balanced even when the friction force dominates the flow. A CFL criterion accounting for the total friction velocity is employed to ensure numerically stable solutions. The comparison of numerical results with analytical solutions and experimental measurements shows that the present HR numerical modeling yields accurate solution near discontinuities beyond the first-order-accurate Godunov-type method that is widely used for modeling debris flows. The evaluation tests reveal that the present method yields numerically stable and efficient solutions of debris flows moving downslope with significant basal friction. The application to two debris flows that were experimentally generated with a fixed-volume and a continuous source reveals that the numerical model reproduces the propagation speed of debris flow on the slopes and the deposition pattern on the fan with reasonable accuracy. Overall results indicate that the present model can provide useful information on transient features of debris flow behavior through the channel with an abrupt change in bottom slope.