Note:

# Numerical Simulation Study of Debris Particles Movement Characteristics by Smoothed Particle Hydrodynamics

## Shoji Ueta^{*,†}, Natsuki Hosono^{**}, Ryusuke Kuroki^{***}, and Yosuke Yamashiki^{*}

^{*}Graduate School of Advanced Integrated Studies in Human Survivability, Kyoto University

1 Nakaadachi-cho, Yoshida, Sakyo-ku, Kyoto, Kyoto 606-8306, Japan

^{†}Corresponding author

^{**}Center for Mathematical Science and Advanced Technology, Japan Agency for Marine-Earth Science and Technology (JAMSTEC), Kanagawa, Japan

^{***}Mizuho Bank, Ltd., Kyoto, Japan

Debris flow is an important natural hazard in mountain zone because it can threaten human lives with very little warning. Since laboratory experiments on debris flows at real scale are difficult to perform, numerical simulations are important in evaluating the impact of such flows. Among several candidate models, the smoothed particle hydrodynamics (SPH) is a particular attractive numerical method for this purpose. SPH is a particle-based numerical hydrodynamic method originally developed in the astrophysical field before extension to elastic bodies. Several works have already tested the applicability of SPH to debris flow, despite there are only few detailed validations. In this report, thus, we aimed to check the applicability of SPH to debris flows. Since the accurate treatment of the elastic bodies tends to be computationally expensive, we have developed a massively parallel SPH code. A comparison between laboratory experiments and numerical simulations using SPH showed qualitatively similar features, though there are differences in quantitive comparisons.

*J. Disaster Res.*, Vol.17, No.2, pp. 237-245, 2022.

- [1] S. Egashira, “Prospects of debris flow studies from constitutive relations to governing equations,” J. Disaster Res., Vol.6, No.3, pp. 313-320, 2011.
- [2] Y. Yamashiki et al., “Simulation and calibration of hydro-debris 2D model (HD2DM) to predict the particle segregation processes in debris flow,” J. of Civil Engineering and Architecture, Vol.6, No.6, pp. 690-698, 2012.
- [3] R. A. Gingold and J. J. Monaghan, “Smoothed particle hydrodynamics: Theory and application to non-spherical stars,” Monthly Notices of the Royal Astronomical Society, Vol.181, No.3, pp. 375-389, 1977.
- [4] L. B. Lucy, “A numerical approach to the testing of the fission hypothesis,” The Astronomical J., Vol.82, No.12, pp. 1013-1024, 1977.
- [5] R. B. Canelas et al., “Debris flow modelling with high-performance meshless methods,” Congress on Numerical Methods in Engineering (CMN2015), 2015.
- [6] W. Wang et al., “3D numerical simulation of debris-flow motion using SPH method incorporating non-Newtonian fluid behavior,” Natural Hazards, Vol.81, No.3, pp. 1981-1998, 2016.
- [7] R. Canelas et al., “A generalized SPH-DEM discretization for the modelling of complex multiphasic free surface flows,” 8th Int. SPHERIC Workshop, 2013.
- [8] W. Benz and E. Asphaug, “Impact simulations with fracture. I. Method and tests,” Icarus, Vol.107, No.1, pp. 98-116, 1994.
- [9] X.-J. Ma and M. Geni, “Simulation of droplet impacting on elastic solid with the SPH method,” Mathematical Problems in Engineering, Vol.2015, Article No.350496, 2015.
- [10] M. Iwasawa et al., “FDPS: A novel framework for developing high-performance particle simulation codes for distributed-memory systems,” Proc. of the 5th Int. Workshop on Domain-Specific Languages and High-Level Frameworks for High Performance Computing (WOLFHPC’15), Article No.1, 2015.
- [11] M. Iwasawa et al., “Implementation and performance of FDPS: A framework for developing parallel particle simulation codes,” Publications of the Astronomical Society of Japan, Vol.68, No.4, Article No.54, 2016.
- [12] J. J. Monaghan, “Simulating free surface flows with SPH,” J. of Computational Physics, Vol.110, No.2, pp. 399-406, 1994.
- [13] B. Zanuttigh and A. Lamberti, “Analysis of debris wave development with one-dimensional shallow-water equations,” J. of Hydraulic Engineering, Vol.130, No.4, pp. 293-304, 2004.
- [14] S. Hergarten and J. Robl, “Modelling rapid mass movements using the shallow water equations in Cartesian coordinates,” Natural Hazards and Earth System Sciences, Vol.15, No.3, pp. 671-685, 2015.
- [15] Y. Yamashiki et al., “Experimental study of debris particles movement characteristics at low and high slope,” J. of Global Environmental Engineering, Vol.17, pp. 9-18, 2012.
- [16] H. J. Melosh, “Impact cratering: A geologic process,” Oxford University Press, 1989.
- [17] J. J. Monaghan, “Smoothed particle hydrodynamics,” Annual Review of Astronomy and Astrophysics, Vol.30, pp. 543-574, 1992.
- [18] W. Dehnen and H. Aly, “Improving convergence in smoothed particle hydrodynamics simulations without pairing instability,” Monthly Notices of the Royal Astronomical Society, Vol.425, No.2, pp. 1068-1082, 2012.
- [19] H. Wendland, “Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree,” Advances in Computational Mathematics, Vol.4, No.1, pp. 389-396, 1995.
- [20] J. J. Monaghan et al., “Gravity currents descending a ramp in a stratified tank,” J. of Fluid Mechatronics, Vol.379, pp. 39-69, 1999.
- [21] J. J. Monaghan, “SPH and Riemann solvers,” J. of Computational Physics, Vol.136, No.2, pp. 298-307, 1997.
- [22] D. S. Balsara, “Von Neumann stability analysis of smoothed particle hydrodynamics – suggestions for optimal algorithms,” J. of Computational Physics, Vol.121, No.2, pp. 357-372, 1995.
- [23] J. Barnes and P. Hut, “A hierarchical
*O (N log N)*force-calculation algorithm,” Nature, Vol.324, Issue 6096, pp. 446-449, 1986. - [24] L. Hernquist and N. Katz, “TREESPH: A unification of SPH with the hierarchical tree method,” The Astrophysical J. Supplement Series, Vol.70, pp. 419-446, 1989.
- [25] J. Makino, “A fast parallel treecode with GRAPE,” Publications of the Astronomical Society of Japan, Vol.56, No.3, pp. 521-531, 2004.
- [26] N. Hosono, T. R. Saitoh, and J. Makino, “A comparison of SPH artificial viscosities and their impact on the Keplerian disk,” The Astrophysical J. Supplement Series, Vol.224, No.2, Article No.32, 2016.
- [27] Y. Imaeda and S. Inutsuka, “Shear flows in smoothed particle hydrodynamics,” The Astrophysical J., Vol.569, No.1, pp. 501-518, 2002.
- [28] T. Okamoto et al., “Momentum transfer across shear flows in smoothed particle hydrodynamic simulations of galaxy formation,” Monthly Notices of the Royal Astronomical Society, Vol.345, No.2, pp. 429-446, 2003.
- [29] N. Frontiere, C. D. Raskin, and J. M. Owen, “CRKSPH – A conservative reproducing kernel smoothed particle hydrodynamics scheme,” J. of Computational Physics, Vol.332, pp. 160-209, 2017.
- [30] E. Gaburov and K. Nitadori, “Astrophysical weighted particle magnetohydrodynamics,” Monthly Notices of the Royal Astronomical Society, Vol.414, No.1, pp. 129-154, 2011.
- [31] D. García-Senz, R. M. Cabezón, and J. A. Escartín, “Improving smoothed particle hydrodynamics with an integral approach to calculating gradients,” Astronomy & Astrophysics, Vol.538, Article No.A9, 2012.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.