Physically Based Sand Slide Method in Scour Models Based on Slope-Limited Diffusion

In scour simulation models, a sand slide step is necessary to treat the bed areas where the slope exceeds the angle of repose. This exceedance is due to the fact that the Exner equation does not take into consideration the angle of repose. Methods for sand slide should conserve mass, be based on physics, and give a unique final bed configuration. However, there is no existing method that satisfies all these requirements. Most previous methods use either a modified bed-load transport rate based on bed slope or purely geometric corrections. This work proposes a new method that solves a slope-limited diffusion equation. The diffusivity is conditioned upon bed slope. The method is based on the physics of sand slide and its diffusive nature. Special numerical schemes, linear gradient scheme (LGS) and Gauss nonlinear gradient scheme (GNGS), were tested for the evaluation of bed elevation gradient, which is used in the conditional function for diffusivity. LGS gives severe bed distortion due to the time lag for sand particles to slide in the diagonal direction of mesh. GNGS greatly alleviates this problem by using an extended stencil. The new sand-slide method was implemented in a 3D scour model and tested with two cases. Results show that the new sand slide method, in conjunction with the GNGS scheme or the combination of GNGS and LGS, produces efficient, physically correct, and mesh-independent results. The simulated scour hole development compares well with the experiment.