# ijege-13_bs-franz-et-alii.pdf

*Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università*

*Editrice*

*DOI: 10.4408/IJEGE.2013-06.B-39*

**LANDSLIDE-TRIGGERED TSUNAMI MODELLING IN ALPINE LAKES**

**INTRODUCTION**

*http://www.ngdc.*

noaa.gov/nndc/struts/form?t=101650&s=70&d=7);

noaa.gov/nndc/struts/form?t=101650&s=70&d=7

S

to this phenomenon due to steep topography and as-

sociated slope instabilities, as well as large amount

of water body such as lakes, fjords or reservoirs.

Moreover, the fact that the valleys are highly popu-

lated and that they concentrate the water flow, give

to this type of region a particularly high potential of

catastrophic events.

volumes range from 5’000 to 300’000 m

leading to an 8 m run-up in Geneva, more than 70

km away from the source (K

*et alii*, 2012).

that occurred in the Alps is the one of Vajont which

involved a 260 x 106 m

NOAA Tsunami Events catalogue shows how little it

is known or studied l

**ABSTRACT**

modelling based on shallow water equations repre-

sents a valuable tool able to provide prediction in

order to assess this threat. However, some inherent

numerical problems (e.g. artefacts development when

applied to real cases, difficulty for wet to dry bed

transition) are well known, but not resolved yet. Our

main objective is to find a method that is relevant for

landslide-triggered tsunami modelling, as accurate as

possible in order to use it as predictive tool.

lution bathymetry. Accordingly, four Godunov-type

solvers are confronted to the exact solution. Interesting-

ly, at high resolution, which is needed for bathymetry,

the difference between monotonous first-order meth-

ods gradually disappears. The simplest Lax-Friedrichs

scheme is suggested as the method of choice. The

experiment of a 2D circular dam break, solved using

Lax-Friedrichs scheme, is presented and the resolution

at which results are converging is reported. Perform-

ance of high resolution 2D runs on CPU and GPU are

reported, documenting 50 fold speedup on GPU. As

result of this speedup, the high resolution run take less

than an hour on GPU card that cost less than 1000 SFr.

**K**

**ey**

**words****:**

*landslide triggered generated tsunami dam lake Alps*

*modelling shallow water equations Godunov Lax Friedrichs GPU*

*M. FRANZ, Y. PODLADCHIKOV, M. JABOYEDOFF & M-H. DERRON*

*International Conference Vajont 1963-2013. Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013*

*F*

*ig. 1 - The left wave and the right wave (S*

*l*

*and S*

*r*

*as ve-*

*locity) that can be rarefaction or shock waves. The*

*middle is a contact wave (S*

*m*

*as velocity)*

*x*

*=*

*x*

*i+1/2*

*between cells*

*i*and

*i+1.*

*F*

*i+1/2*

*GODUNOV UPWIND*

waves is the star region. In this region h and u are

characterized by h* u*, for which a nonlinear algebra-

ic equation is solved by an iterative method. The flux

of the Godunov upwind scheme (Gup) is computed

for the exact local Riemann solution

*U*

*i*+1/2

tions were encountered. When applied to real cases,

development of numerical artefacts were reported

(W

*et alii*, 2007; F

*et alii*, 2012). S

algorithm to solve it based on the approximate Rie-

mann solvers allowing for dry bed transition. In K

*et alii*(2012) this approach was applied for real

(i.e. run-up). t

low water equations. More recently, t

front propagation. z

nonlinear shallow water equations are confronted to

numerical difficulties, even with exact Riemann solv-

er. To resolve these numerical difficulties, we reiniti-

ated testing of the various methods described in t

by modern computers. We introduced additional tests

relevant for tsunami imitated by landslides and tests

for treating of variable bathymetry.

**METHODS**

er), the Godunov centred, and the Godunov upwind

(t

*U*the solution vector,

*F*and

*G*the flux vectors

defined as

of the depth-averaged velocity vector, g is the gravity

acceleration. Dimensional splitting is used to reduce it

to the augmented one-dimensional problem

**LANDSLIDE-TRIGGERED TSUNAMI MODELLING IN ALPINE LAKES**

*Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università*

*Editrice*

*Generation of a dry bed (test 5)*

aperture reaches the bed and spontaneously generates

a dry bed. It tests the capacity of the codes to generate

a dry bed condition from a wet bed. It is considered as

the most difficult of the five tests (Tab. 2, test 5).

sive to be used in practice (t

points. Moreover it is not oscillating and generally fits

correctly the exact solution. The LF scheme, due to its

simplicity, can be the best choice in order to model wave

generation and propagation over complex bathymetry.

*GROUP 2: ADDITIONAL TESTS FOR LANDSLI-*

DE-GENERATED TSUNAMI

DE-GENERATED TSUNAMI

velocity jump potentially leading to the spontaneous

formation of the dry state (like in tests 2 and 5). Simi-

larly to the tests 2 and 5, we introduce tests 6 and 7 in

such a way that test 6 does not lead to the spontaneous

dry state while test 7 does. Tests 6 and 7 are different

from tests 2 and 5 by allowing for a water level jump

in initial conditions. These additional tests are relevant

for the landslide-generated tsunami. Indeed, sliding

into shallow water landslide can be accommodated by

water level elevation on the top of the landslide and

divergent horizontal velocity laterally displacing the

water and creating the space for the landslide. The lat-

ter possibility may potentially lead to the spontaneous

generation of the dry state. Newly suggested tests 6

and 7 are proposed as a validation for the ability of a

numerical scheme to handle and to correctly predict

the spontaneous dry state around landslide.

**TESTS**

the dam break. As we are interested in landslide gener-

ated waves, we add three additional tests (6, 7 and 8 in

Tab. 2) that better capture the generation of the wave

by the penetration of a landslide in the water body.

*GROUP 1: THE TORO (2001) TESTS*

Left critical Rarefaction and Right Shock (test 1)

Left critical Rarefaction and Right Shock (test 1)

oscillations, and the steepness of the front. Initial data

(Tab. 2, test 1) produce shock wave to the right and

rarefaction to the left.

*Two rarefaction and nearly dry bed (test 2)*

tion waves travelling in opposite directions. The water

depth at the created aperture is close to zero. The test

investigates the symmetry of propagation, the ability

of the schemes to sustain the near zero water depth

situation and smoothness of the velocities profiles.

*Right dry bed Riemann problem (test 3)*

tion wave. The test evaluates the capacity of a numeri-

cal scheme to handle the transition from dry to wet bed.

*Left dry bed Riemann problem (test 4)*

efaction wave. The test evaluates the capacity of a

numerical scheme to handle the transition from dry to

wet bed and negative velocities.

*Tab 1 - GPU time for the runs presented at*

*Figure 7 (same physics and model*

*tested but different resolution)*

*Tab 2 - The initial parameters of the*

*tests, where hL, and hR are*

*the water level, u*

*L*

*and u*

*R*

*the*

*velocity, respectively on the*

*left and the right, x*

*0*

*the posi-*

*tion of the wall and Tout the*

*time of the simulation end*

*M. FRANZ, Y. PODLADCHIKOV, M. JABOYEDOFF & M-H. DERRON*

*International Conference Vajont 1963-2013. Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013*

The Figure 4 illustrates this test. The cross section is

assumed perpendicular to the slide direction. For this

test, as for the next two tests, there are only Gup and

the LF schemes are shown.

main relevant aspect is that an increased resolu-

*Test 6: Moderate test of landslide penetration*

(100m depth, 1m/s velocity)

(100m depth, 1m/s velocity)

The initial conditions (Table 2, test 6), as the low ini-

tial velocities, make this test similar to the test n° 1,

where the elevation of water due to the landslide be-

come affected by a rarefaction wave that propagates to

*Fig. 2 - Four methods are com-*

*pared with the exact Rie-*

*mann solution, respec-*

*tively from tests 1 to test 5*

*(from top to bottom) at a*

*resolution of 2000 numer-*

*ical grid points. At such a*

*resolution, all the meth-*

*ods fit quite well to exact*

*solution. The LF is the*

*most numerically diffused*

*solution (velocity & eleva-*

*tion). There are only two,*

*LF and Gup, that show no*

*numerical oscillations*

*Fig. 3 - Close-ups on the shock waves (elevation and velocity) of the test 1.Left: grid resolution is 500; Right: grid resolution is 2000.*

*Only Gup and LF schemes are not oscillatory. The LF is the most diffusive solution, but it captures the wave location well*

**LANDSLIDE-TRIGGERED TSUNAMI MODELLING IN ALPINE LAKES**

*Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università*

*Editrice*

*Test 8: a rough bed*

bed (Fig. 6). This is a crucial point for a reliable nu-

merical model for landslide-generated tsunami over

real bathymetry. The Gup and the LF methods suc-

cessfully passed this rough bed test (Fig. 6). Again

the solutions at higher resolution are less diffusive.

Moreover, both schemes have passed the consist-

ency test: rough bathymetry does not cause wave

motion if the water level is flat and initial velocity

is zero. We conclude that both schemes are admis-

sible while having similar computational cost. LF

is preferred due to considerable simplicity of its

implementation.

cal schemes and reduces the difference between the

two numerical solutions.

*Test 7: Extreme test of landslide penetration (0.1 m*

depth, 6 m/s velocity)

depth, 6 m/s velocity)

except that the water is very shallow (0.1 m) and the

initial velocity is faster (6 m/s). The initial data (Table

2, test 7) induce lateral displacement of the water lead-

ing to a spontaneous dry state like test 5.

diffusion with a higher resolution (here 2000).

*Fig. 5 - Results of the extreme test 7 for Gup and*

*LF methods. Top: grid resolution is 200;*

*Bottom: grid resolution is 2000*

*Fig. 4 - Results of the moderate test 6 for Gup*

*and LF methods. Top: grid resolution is*

*200; Bottom: grid resolution is 2000*

*M. FRANZ, Y. PODLADCHIKOV, M. JABOYEDOFF & M-H. DERRON*

*International Conference Vajont 1963-2013. Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013*

*GROUP 3: RESOLUTION TESTS IN 2D*

lution on the numerical diffusivity of the simplest LF

scheme. They are performed on a regular worksta-

tion to check if needed high resolution is practically

achievable. The Figure 7 presents the results of the

exactly the same experimental setup (circular dam

break) conducted at different grid resolutions.

time rises with the resolution (see Table 1). We ob-

serve that GPU computing is practical already

**SUMMARY**

merical schemes considered. Despite the fact that the

LF method is commonly regarded as too diffusive

and not practical (e.g. t

best solutions, considering that they are not oscillato-

ry. The groups 2 and 3 continued the testing with only

these two methods. In our second testing suit (group

2) consisting of tests 6, 7 and 8, we have considered

more difficult numerical scenarios related to land-

slides-triggered tsunami problems. Running these

tests with different resolutions, it appears clearly that

a higher resolution solves the diffusive problems. The

test 8 demonstrates robustness of both LF and Gup

over rough bed. Finally, the tests of the group 3 shows

models, when computed on GPU.

od can be a good choice because: it is not oscillatory,

its diffusive problems disappear with high resolution,

it withstands rough beds, and its simplicity.

**CONCLUSION**

Modelling this phenomenon is necessary in order to

assess its consequences, but it is known to be prob-

*Fig. 6 - Results of the rough bed test 8 for Gup*

*and LF methods. Top: grid resolution is*

*200; Bottom: grid resolution is 2000*

*Fig. 7 - Results of four resolution tests in 2D*

**LANDSLIDE-TRIGGERED TSUNAMI MODELLING IN ALPINE LAKES**

*Editrice*

Friedrichs method. Indeed, with modern high resolu-

tion computing, this method is no more too diffusive,

captures correct propagation velocities, non-oscilla-

tory and easy to implement.

ods with the exact Riemann solution, proposes three

new tests directly linked to the landslide-generated

tsunami and investigates the effects and the feasi-

bility of (very) high resolution 2D modelling tests.

**REFERENCES**

*Numerical modelling of a landslide-*

*generated tsunami: the 1979 Nice Event.*Pure appl. Geophys.,

**157**: 1707-1727.

*Shallow water numerical model of the wave generated by the Vajont landslide.*Environmental

**26**: 406-418.

*Tsunami in Alps reservoirs: the case of Mauvoisin dam (Valais, Switzerland).*Geophysical Research Abstracts,

**14**. EGU

General Assembly 2012.

*Preliminary hydrodynamic analysis of landslide-generated waves*

*in Tidal Inlet, Glacier Bay National Park, Alaska.*U.S. Geological survey Open-File Report 03-411.

*Simulation of landslide-generated*

*tsunamis with the HySEA platform: application to the Lituya Bay 1958 tsunami.*Geophysical Research Abstracts,

**14**. EGU

General Assembly 2012.

*Landslide generated impulse waves in reservoirs: basics and computation.*

*Felsbewegungen und Uferabbrüche an Schweizer Seen, ihre Ursachen und Auswirkungen.*Eclogae

**75**(3): 563-578.

*Giant Lake Geneva tsunami in ad 563.*Nature Geoscience,

**5**: 756-757.

*The 1888 shoreline landslide and tsunami in*

*Trondheimsfjorden, central Norway.*Mar. Geophys. Res.,

**32**: 313-329.

*Bürgenstock Ehemaliger Steinbruch Obermatt, Gefahren- und Sicherheitsbeurteilung.*Louis

*A numerical study of submarine-landslide-generated waves and run-up.*Proc. R. Soc. Lond.,

**458**:

*A two-layer approach to wave modelling.*Proc R. Soc. Lond.,

**460**: 2637-2669.

*Experiments with MATLAB.*Electronic edition published by MathWorks, Inc.

*Coupling between shallow water and solute flow equations:*

*analysis and management of source terms in 2D.*Int. J. Numer. Meth. Fluids,

**49**: 267-299.

*A real two-phase submarine debris flow and tsunami.*American Institute of Physics

**1479**: 197-200.

*Characteristic-based schemes for the Euler equations.*Ann. Rev. Fluid Mech.,

**18**: 337-365.

*History of the 1963 Vaiont slide: the importance of geological factors.*Bull. Eng. Geol.

**59**: 87-97.

*Coupled model of surface water flow, sediment transport and morphological evolution.*

**32**: 1600-1614.

*Occurrences, properties, and predictive models of landslide-generated water waves.*In:

*Rockslide and avalanches*. Vol. 2: 317-397, Elsevier, Amsterdam.

*The landslides and tsunamis of the 30th of December 2002 in Stromboli analysed*

*through numerical simulations.*Bull. Volcanol.,

**68**: 462-479.

*Shock-capturing methods for free-surface shallow flows.*Wiley, New York.

*Godunov-type methods for free-surface shallow flows: A review.*Journal of Hydraulic

**45**: 736-751.

*M. FRANZ, Y. PODLADCHIKOV, M. JABOYEDOFF & M-H. DERRON*

*The 1963 Landslide and Flood at Vajont Reservoir Italy. A tsunami ball simulation.*Ital.J.Geosci.,

**130**: 16-26.

*Preliminary assessment of landslide-induced wave*

*hazards: Tidal Inlet, Glacier Bay National Park, Alaska.*U.S. Geol. Survey Open-File Report 03-100.

*Hazard assessment of the Tidal Inlet landslide and potential*

*subsequent tsunami, Glacier Bay National Park, Alaska.*Landslides.

*Efficient computation of surf zone waves using nonlinear shallow water equations with*

*non-hydrostatic pressure.*Costal Engineering,

**55**: 780-790.