Granular Flow–Obstacle Interaction and Granular Dam Break Using the S-H Model with the TVD-MacCormack Scheme

Abstract

An accurate second-order spatial and temporal finite-difference scheme is applied to solve the dynamics model of a depth-averaged avalanche. Within the framework of the MacCormack scheme, a total variation diminishing term supplements the corrector step to suppress large oscillations in domains with steep gradients. The greatest strength of the scheme lies in its high computational efficiency while maintaining satisfactory accuracy. The performance of the scheme is tested on a granular flume flow–obstacle interaction scenario and a granular dam breaking scenario. In the former, the flume flow splits into two granular streams when an obstacle is encountered. The opening between the two granular streams widens when the side length of the obstacle increases. In the simulation, shock waves with a fan-shaped configuration are captured, and successive waves in the tail of the avalanche between the two streams are observed. In the latter scenario, the average values and the fluctuations in the flow rate and velocity (at relatively steady state) decrease with the width of the breach. The capture of complex and typical granular-flow phenomena indicates the applicability and effectiveness of combining the TVD-MacCormack Scheme and S-H model to simulate dam breaking and inclined flow–obstacle interaction cases. In this study, the dense granular flow strikes on a rigid obstacle that is described by a wall boundary, rather than a topographic feature with a finite slope. This shows that the TVD-MacCormack scheme has a shock-capturing ability. The results of granular dam break simulations also revealed that the boundary conditions (open or closed) affect the collapse of the granular pile, i.e., the grains evenly breached out under closed boundary conditions, whereas the granules breaching out of the opening were mostly grains adjacent to the boundaries under open boundary conditions.

Keywords

• finite-element scheme
• granular flow
• avalanche
• dynamic model
• interaction