Two-dimensional numerical simulation of debris flow based on diffusion wave method considering continuity and time-step dependency

Abstract

This study presents a novel 2D numerical simulation model for debris flow based on diffusion wave equation considering the continuity and time-step dependency. A congenital problem of the diffusion wave equation is the numerical instability which collapses the continuity law of water and sediment, because the diffusion wave equation does not represent the acceleration and deceleration process of the dynamic flow. To overcome this disadvantage the present study proposes a new numerical scheme called correcting continuity equation (CCE) method that allows for avoiding the continuity issue. The numerical model was verified in a past debris flow event that occurred in Japan. The numerical model well simulated overall pattern of the deposition height and water surface elevation observed in the debris flow event. Furthermore, the CCE approach was found to satisfy the continuity of water and sediment completely. In addition, the numerical result implied importance of stability condition considering both advection and diffusion property of the diffusion wave equation.