A spectral multidomain penalty method solver for the numerical simulation of granular avalanches

This work presents a high-order element-based numerical simulation of an experimental granular avalanche, in order to assess the potential of these spectral techniques to handle geophysical conservation laws. The spatial discretization of these equations was developed via the spectral multidomain penalty method (SMPM). The temporal terms were discretized using a strong-stability preserving Runge-Kutta method. Stability of the numerical scheme is ensured with the use of a spectral filter and a constant or regularized lateral earth pressure coefficient. The test case is a granular avalanche that is generated in a small-scale rectangular flume with a topographical gradient. A grid independence test was performed to clarify the order of the error in the mass conservation produced by the treatments here implemented. The numerical predictions of the granular avalanches are compared with experimental measurements performed by Denlinger and Iverson (2001). Furthermore, the boundary conditions and parameters such as lateral earth pressure coefficients and the momentum correction factor were analyzed in order to observe the incidence of these features when solving the granular flow equations. This work identifies the benefits and weaknesses of the SMPM to solve this set of equations, and thus, it is possible to conclude that the SMPM provides an appropriate solution to the granular flow equations proposed by Iverson and Denlinger (2001) and comparable predictions for the experimental data.