以CUDA架構進行地形座標系統上之三相流模式GPU計算

MODELING THREE‐PHASE DEBRIS FLOWS IN TERRAIN-FOLLOWING COORDINATE SYSTEM AND ITS GPU COMPUTATION WITH CUDA STRUCTURE

10.6652/JoCICHE.202211_34(7).0004

馬晴元(Ching-Yuan Ma)；柯奇均(Chi-Jyun Ko)；王福杰(Hock-Kiet Wong)；戴義欽(Yih-Chin Tai)

三相流土石流模型 ； 地形座標系統 ； CUDA ； GPGPU ； three-phase debris flow model ； terrain coordinates ； CUDA ； GPGPU

中國土木水利工程學刊

34卷7期（2022 / 11 / 01）

597 - 604

英文

土石流災害危險評估中，其運移特性及影響範圍為探討之要點。由於土石流的組成複雜，過往的研究往往因計算的繁複而以單相流或是二相流的理論模型進行模擬計算其運移行為，所能模擬之情境有所限制，如間隙流體的黏滯性會因懸浮細顆粒的濃度改變產生顯著的變化。本研究採用地形座標上的三相流理論之數值模式，可描述濃度較高之土砂自陡坡滑入河道後，與濃度較低之河水相混合後之動態行為。模擬之結果顯示，下滑之土體不僅推移河道中之水體產生湧浪，水面上溯入侵對岸導致氾濫。此外，本研究的數值模式採用CUDA架構進行GPU高效率即時演算，深具防災工程應用情境探討的潛力。

In terms of disaster assessment for the debris flows, the characteristics of flow behaviors and the associated flow paths are the main concerns. Despite the complex composition of debris flow, models of single-phase or two-phase approaches are employed for the purpose of reducing the computational expense. This practice has highly limited the capability of describing various scenarios because the concentration of the suspended fine clay/silt significantly influences the viscosity of the interstitial fluid. In the present study, a three-phase (solid, clay/silt, and water) model for debris flows is suggested, which is given in the terrain-following coordinate system. With this three-phase approach, the merging of high-density debris flows into the river can be well described, where a surge is induced, and the water level is enhanced together with intrusion into the opposite bank. In addition, the associated numerical model is implemented with the CUDA structure for GPU computation. The high efficiency exhibits the powerful capability of real-time calculation, yielding the impressive potential for engineering applications with respect to scenario investigation.

1. Baumgarten, A. S.,Kamrin, K.(2019).A general fluid–sediment mixture model and constitutive theory validated in many flow regimes.Journal of Fluid Mechanics,861,721-764.
2. Berzi, D.,Jenkins, J. T.(2008).A theoretical analysis of free-surface flows of saturated granular-liquid mixtures.Journal of Fluid Mechanics,608,393-410.
3. Berzi, D.,Jenkins, J. T.(2009).Steady inclined flows of granular-fluid mixtures.Journal of Fluid Mechanics,641,359-387.
4. Chow, V. T.(1959).Open channel hydraulics.New York:McGraw-Hill.
5. Coussot, P.,Piau, J. M.(1994).On the behavior of fine mud suspension.Rheologica Acta,33,175-184.
6. Egashira, S.,Ashida, K.(1992).Unified view of the mechanics of debris flow and bed-load.Advances in micromechanics of granular material, in series Studies in Applied Mechanics,31,391-400.
7. Egashira, S.、Ashida, K.、Yajima, H.、Takahama, J.(1989)。Constitutive equation of debris flow。Ann. D.P.R.I., Kyoto Univ.，32B-2，487-501。
8. Egashira, S.,Miyamoto, K.,Itoh, T.(1997).Constitutive equations of debris flow and their applicability.Proc. of 1st International Conference on Debris-flow Hazards Mitigation,New York:
9. Harris, M.(2007).Optimizing parallel reduction in CUDA.NVIDIA Developer Technology,2(4),70.
10. Huang, X.,Garcia, M. H.(1998).A Herschel-Bulkey model for mud flow down a slope.Journal of Fluid Mechanics,374,305-333.
11. Iverson, R. M.(1997).The physics of debris flows.Rev. Geophys.,35,245-296.
12. Iverson, R. M.,Denlinger, R. P.(2001).Flow of variably fluidized granular masses across three-dimensional terrain. Part I Coulomb mixture theory.J. Geophys. Res.,106,537-552.
13. Ko, C. J.,Chen, P. C.,Wong, H. K.,Tai, Y. C.(2021).,未出版
14. Kurganov, A.,Tadmor, E.(2000).New high-resolution central schemes for nonlinear conservation laws and convection–diffusion equations.Journal of Computational Physics,160(1),241-282.
15. Liu, K. F.,Mei, C. C.(1989).Slow spreading of a sheet of Bingham fluid on an inclined plane.Journal of Fluid Mechanics,207,505-529.
16. Luca, I.,Tai, Y. C.,Kuo, C. Y.(2016).Shallow Geophysical Mass Flows down Arbitrary Topography.Springer Verlag.
17. Meng, X.,Johnson, C.,Gray, J.M.N.T.(2022).Formation of dry granular fronts and watery tails in debris flows.Journal of Fluid Mechanics,943,A19.
18. Meng, X.,Wang, Y.(2016).Modelling and numerical simulation of two-phase debris flows.Acta Geotechnica,11(5),1027-1045.
19. Nishiguchi, Y.,Uchida, T.(2022).Long‐Runout‐Landslide‐Induced Debris Flow: The role of fine sediment deposition processes in debris flow propagation.Journal of Geophysical Research: Earth Surface,127(2),e2021JF006452.
20. Nishiguchi, Y.,Uchida, T.,Tamura, K.,Satofuka, Y.(2011).Prediction of run-out process for a debris flow triggered by a deep rapid landslide.Proceedings of the 5th debris flow hazard mitigation conference,Padua, Italy:
21. O’Brien, J. S.,Julien, P. Y.(1988).Laboratory analysis of mudflow properties.ASCE Journal of Hydraulics Engineering,114,877-887.
22. Pitman, E. B.,Le, L.(2005).A two-fluid model for avalanche and debris flows.Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences,363(1832),1573-1601.
23. Pudasaini, S. P.(2012).A general two‐phase debris flow model.Journal of Geophysical Research: Earth Surface,117(F3)
24. Pudasaini, S. P.,Mergili, M.(2019).A multi‐phase mass flow model.Journal of Geophysical Research: Earth Surface,124(12),2920-2942.
25. Tai, Y. C.,Heß, J.,Wang, Y.(2019).Modeling Two‐Phase Debris Flows With Grain‐Fluid Separation Over Rugged Topography: Application to the 2009 Hsiaolin Event, Taiwan.Journal of Geophysical Research: Earth Surface,124(2),305-333.
26. Tai, Y. C.,Kuo, C. Y.(2012).Modelling shallow debris flows of the Coulomb-mixture type over temporally varying topography.Natural Hazards and Earth System Sciences,12(2),269-280.
27. Tai, Y. C.,Kuo, C. Y.,Hui, W. H.(2012).An alternative depth-integrated formulation for granular avalanches over temporally varying topography with small curvature.Geophys. Astrophys. Fluid Dyn.,106(6),596-629.
28. Takahashi, T.(2014).Debris flow: mechanics, prediction and countermeasures.Taylor & Francis Group.