Numerical Simulation of Debris Avalanche Problems

Sudi MungkasiDepartment of Mathematics,

Sanata Dharma University, YogyakartaEmail: sudi@usd.ac.id

Outline of presentation

• Introduction of the problem• Method to solve the problem• Research results• Conclusion

Introduction: Motivation

Flood at bundaran air mancur near Patung Arjuna Wiwaha Jalan MH Thamrin Jakarta Monday 9/2/2015 Source: http://megapolitan.kompas.com/read/2015/02/09/22452411/FOTO.Ibu.Kota.yang.Pasti.Tenggelam

Introduction: Motivation

Landslide in Sukabumi in March 2015. At least 12 people died. http://news.okezone.com/read/2015/03/29/340/1126082/longsor-di-sukabumi-12-

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Introduction: Goal

• Our goal is to promote doing a numerical simulation of disasters before they occur.

• In this work, we focus on avalanche problems, such as landslides, debris avalanche, snow avalanche, etc.

• We will use ANUGA software to do simulations and assess its performance.

Outline of presentation

• Introduction of the problem• Method to solve the problem• Research results• Conclusion

Method

• The shallow water equations to model water flows are in the following form:

where q is the quantity vector, f and g are the flux vectors, and s is the source.

Numerical Method: Finite Volume Method for 1 Dimension

Numerical Method: Finite Volume Method for 1 Dimension

Numerical Method: Finite Volume Method for 2 Dimensions

Numerical Method: Finite Volume Method for 2 Dimensions

Metode volume hingga untuk dua dimensi dengan diskritisasi segitiga mempunyai skema:

atau

Numerical Method

• Finite volume method with triangular grids is used to solve the shallow water equations:

• This method has been programmed in ANUGA package. ANUGA is a free and open source software developed by Australian National University (ANU) and Geoscience Australia (GA).

Outline of presentation

• Introduction of the problem• Method to solve the problem• Research results• Conclusion

Example of ANUGA simulation

ANUGA tsunami simulation for Wollongong east coast by SG Roberts

Wet/dry avalanche

Avalanche problems: initial condition

Wet/wet avalanche

Avalanche problems: numerical results

Wet/dry avalanche Wet/wet avalanche

Avalanche problems: numerical results

Wet/dry avalanche Wet/wet avalanche

Conclusion

• We have tested the performance of ANUGA software to solve debris avalanche problems.

• It is also robust, as it can deal with dry areas and shock waves with relatively coarse discretization of the topography.

• For future research direction, case studies can be conducted, such as snow avalanche and landslide.

References• A. Mangeney, P. Heinrich, & R. Roche, "Analytical solution for testing debris avalanche

numerical models," Pure and Applied Geophysics, vol. 157, pp. 1081-1096, 2000.• S. Mungkasi & S. G. Roberts, "A new analytical solution for testing debris avalanche numerical

models," ANZIAM Journal, vol. 52, pp. C349-C363, 2011.• S. Mungkasi & S. G. Roberts, "Analytical solutions involving shock waves for testing debris

avalanche numerical models," Pure and Applied Geophysics, vol. 169, pp. 1847-1858, 2012.• M. Naaim, S. Vial, & R. Couture, "Saint Venant approach for rock avalanches modelling," In

Proc. Saint Venant Symposium: Multiple Scale Analyses and Coupled Physical Systems, Presses de l'Ecole Nationale des Ponts et Chausees Paris (1997), pp. 61-69.

• A. Ritter, "Die fortpflanzung der wasserwellen," Zeitschrift des Vereines Deutscher Ingenieure, vol. 36, pp. 947-954, 1892.

• S. Roberts, O. Nielsen, D. Gray, & J. Sexton, ANUGA User Manual, Canberra: Commonwealth of Australia (Geoscience Australia) and The Australian National University, 2010.

• J. J. Stoker, Water Waves: The Mathematical Theory with Applications, New York: Interscience, 1957.

Thank you