# Liu et al benchmark

### From Gerris

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== 2D/3D Comparisons == | == 2D/3D Comparisons == | ||

- | Preliminary simulation were run in two-dimension. Great agreement is not expected but this is a useful step to go through to assess the behavior of the code and tune the simulation. Even though the scale are slightly different between the plots of the 3D and 2D simulation presented hereafter, it is possible to see that 2D and 3D simulations remain more or less similar during the first half of the simulation. Then wave-breaking occurs with accompanies with a dampening of the wave height in the 3D case, which is not the case in the 2D simulation. | + | Preliminary simulations were run in two-dimension. Great agreement is not expected but this is a useful step to go through to assess the behavior of the code and tune the simulation. Even though the scale are slightly different between the plots of the 3D and 2D simulation presented hereafter, it is possible to see that 2D and 3D simulations remains qualitatively more or less similar during the first half of the simulation. Then wave-breaking occurs with accompanies with a dampening of the wave height in the 3D case, which is not the case in the 2D simulation. |

+ | |||

+ | Globally the wave height in 2D are much larger than in 3D or in the laboratory experiments which is not a surprise as momentum cannot travel in the transverse direction. The strong wave-breaking found in 2D makes the wave height at the different gauges hard to assess, but the arrival time of the first wave seem to be predicted well enough while the wave amplitude from the start are two to three time large than what is found in reality. | ||

+ | |||

{| align="center" | {| align="center" |

## Revision as of 20:24, 23 March 2011

This benchmark for simulations of landslide-generated tsunamis using Gerris is based on these articles:

*P. L.-F. Liu, T.R. Wu, F. Raichlen, C.E. Synolakis, J. C. Borrero* - **Runup and rundown generated by three-dimensional sliding masses**

- Journal of Fluid Mechanics 536:107-144, 2005
- Bibtex

*S. Abadie, D. Morichon, S. Grilli, S. Glockner* - **Numerical simulation of waves generated by landslides using a multiple-fluid Navier-Stokes model**

- Coastal Engineering 57:779-794, 2010
- Bibtex

We focus here on one of the configuration that was retained as one of the benchmark test of the third international workshop on long-wave runup models (run 30). We look at the wave created by the free fall of a half-rectangle slide along a uniform slope.

The design of this page is inspired from that dedicated to the Enet_et_al_benchmark.

## Contents |

## Generating the landslide body geometry

A GTS surface representation of the slide has to be generated to be fed to the moving boundary implementation GfsSolidMoving. This can be done using the following script:

# Generates the points of the triangulation

awk -f liu.awk > points.tmp

# Generates and rotates the triangulation

( wc points.tmp | awk '{print $1" 0 0"}'; cat points.tmp ) | delaunay -d | transform --rx=-90 > liu.gts

The awk script 'liu.awk' allows to generate the points of the triangulation. The notations a and b correspond to that of (Liu et al., 2005)

BEGIN {

a=0.4572

b=0.9144

alpha=atan2(a,b);

h=a*cos(alpha);

l1=b*cos(alpha);

l2=a*sin(alpha);

for (k=0; k <= 100; k++) {

for (i=-10; i <= 100; i++) { printf("%5.4f %5.4f %5.4f\n",l1*i/100, -0.5+k/100 , h*i/100) }

for (i=1; i <= 110; i++) { printf("%5.4f %5.4f %5.4f\n",l1+l2*i/100, -0.5+k/100, h*(1-i/100)) }

}

dx=1.0e-4

k=0.

j=-10.

for (i=-10; i <= 100; i++) { printf("%5.4f %5.4f %5.4f\n",l1*i/100, -0.5+k/100-dx,h*j/100) }

for (i=1; i <= 110; i++) { printf("%5.4f %5.4f %5.4f\n",l1+l2*i/100, -0.5+k/100-dx,h*j/100) }

k=100.

for (i=-10; i <= 100; i++) { printf("%5.4f %5.4f %5.4f\n",l1*i/100, -0.5+k/100+dx,h*j/100) }

for (i=1; i <= 110; i++) { printf("%5.4f %5.4f %5.4f\n",l1+l2*i/100, -0.5+k/100+dx,h*j/100) }

}

## Numerical "wave gauge"

[ The setup of the numerical gauges is identical to that of Enet_et_al_benchmark. Please see Enet_et_al_benchmark for more details. Only the location of the gauges and the angle of the slope angle have to be modified. Consequently the 'distance.awk' which is used to calculate the surface elevation becomes:

BEGIN {

tant = 0.4572/0.9144

norm = sqrt (1. + tant*tant)

FS=" |:"

}

{

if ($1 == "#") {

# get column indices of the relevant fields (X,Y)

for (i = 1; i <= NF; i++) {

if ($i == "T")

iT = $(i-1);

else if ($i == "X")

iX = $(i-1);

else if ($i == "Y")

iY = $(i-1);

}

}

else {

T = $iT

if (T > 0. && T < 1.) {

# the cell contains an interface

x = $iX

y = $iY

print $1,(y - tant*x)/norm;

fflush (stdout);

}

}

}

and the coordinates of the probe 'wires' can be generated using the awk script:

BEGIN {

angle = atan2(0.4572,0.9144)

for (y = -0.1; y <= 0.1; y+= 0.001) {

x = 1.83

print cos(angle)*x - sin(angle)*y, sin(angle)*x + cos(angle)*y, 0 > "probe1x"

x = 1.2446

print cos(angle)*x - sin(angle)*y, sin(angle)*x + cos(angle)*y, 0.635 > "probe2x"

x = 0

print cos(angle)*x - sin(angle)*y, sin(angle)*x + cos(angle)*y, 0 > "probe3x"

x = 0

print cos(angle)*x - sin(angle)*y, sin(angle)*x + cos(angle)*y, 0.305 > "probe4x"

x = 0

print cos(angle)*x - sin(angle)*y, sin(angle)*x + cos(angle)*y, 0.61 > "probe5x"

}

}

## 3D Results

So far, I still have problems related to the VOF interface and the simulation crashes after 1.2 time units (a bit more than a third of the simulation). Hopefully this is only a matter of more tunning. Preliminary results are promising.

## 2D/3D Comparisons

Preliminary simulations were run in two-dimension. Great agreement is not expected but this is a useful step to go through to assess the behavior of the code and tune the simulation. Even though the scale are slightly different between the plots of the 3D and 2D simulation presented hereafter, it is possible to see that 2D and 3D simulations remains qualitatively more or less similar during the first half of the simulation. Then wave-breaking occurs with accompanies with a dampening of the wave height in the 3D case, which is not the case in the 2D simulation.

Globally the wave height in 2D are much larger than in 3D or in the laboratory experiments which is not a surprise as momentum cannot travel in the transverse direction. The strong wave-breaking found in 2D makes the wave height at the different gauges hard to assess, but the arrival time of the first wave seem to be predicted well enough while the wave amplitude from the start are two to three time large than what is found in reality.