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

Mario Germán Trujillo-Vela,Alfonso Mariano Ramos-Cañón,Jorge Alberto Escobar-Vargas

doi:10.15446/esrj.v23n4.77683

Mario Germán Trujillo-Vela, Alfonso Mariano Ramos-Cañón + Show 1 more

Open Access

https://doi.org/10.15446/esrj.v23n4.77683

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Abstract

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 conservation laws in geophysics. 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 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 & Iverson (2001). Furthermore, the boundary conditions and parameters such as lateral earth pressure coefficients and the momentum correction factor were analyzed 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, it is possible to conclude that the SMPM provides an appropriate solution of the granular flow equations proposed by Iverson & Denlinger (2001). Besides, it produces comparable predictions to experimental data and numerical results given by other schemes.

Highlights

The study of granular avalanches provides a basis for understanding a variety of mass movements, such as rock avalanches, snow avalanches, debris flows and pyroclastic flows Denlinger and Iverson (2001)
Results using methods of low order are reported by Gray et al, (1999), Hutter and Koch, (1991), Hutter and Greve, (1993), Hutter et al, (2005), Ouyang et al, (2013), Savage and Hutter, (1989), Tai et al, (2002), Wieland et al, (1999), Denlinger and Iverson, (2001), Denlinger and Iverson, (2004), Koschdon and Schafer, (2003), Vollmoller, (2004), Wang et al, (2004), where the numerical solution shows a similar structure when compared with experimental data
Numerical prediction spectral multidomain penalty method (SMPM), = 0.93 s a) Experiment ( D-I2001 ), = 1.50 s b) Numerical prediction SMPM, = 0.50 s method employed in order to obtain an optimal grid

Summary

Introduction

The study of granular avalanches provides a basis for understanding a variety of mass movements, such as rock avalanches, snow avalanches, debris flows and pyroclastic flows Denlinger and Iverson (2001). We propose that future research examine this parameter in order to generate a momentum correction factor that can change depending on what period of movement is being examined when the shallow water approach is used

Discussion

Conclusions