Liu et al benchmark

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Revision as of 20:54, 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.

1 Generating the landslide body geometry
2 Numerical "wave gauge"
3 3D Results
4 2D/3D Comparisons
5 Gerris parameter file 'liu.gfs'
6 GfsView3D file 'view3D.gfv'

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, the full simulations I have managed to run give reasonable results. Those can be commented in the light of Stephane's previous comment on the Enet_et_al_benchmark. Wave gauge comparisons are possibly better for this test case, but we can observe the same trends in the results i.e. the over-prediction of the wave amplitude and the simulation is slightly late on the first trough. While this might not appear to be very satisfactory, this is as good as the results of (Abadie et al., 2010).

Wave generation is generally mainly governed by pressure forces and as a first approximation it was assumed that the fluids here are inviscid. In order to assess whether the validation on this benchmark test can be improved to more runs will be made: one with viscous fluids and a second one with a better resolution.

Evolution in time of the VOF interface for a simulation with adaptive refinement down to level 8
0.6 s	1.0 s	1.4 s
1.8 s	2.2 s	2.6 s

Comparison of the evolution of wave height with time with the measurements of (Liu et al., 2005) at two locations
Gauge 1	Gauge 2

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.

Comparison between 2D simulations (right) and the central cross-section of the 3D simulations for similar resolution. From top to bottom snapshots are for time = 0.6, 1.0, 1.4, 1.8, 2.2 and 2.6 s.

Gerris parameter file 'liu.gfs'

The simulation can be run using: gerris3D -m liu.gfs

Define LEVEL 8
Define LMIN 4
Define RHO MAX(0.01, (0.01*T + (1. - T)))
Define ANGLE (atan2(0.4572,0.9144))
 
2 1 GfsSimulationMoving GfsBox GfsGEdge { y = 0.5 } {
 
    # Sets the duration of the simulation to 3 time units
    Time { end = 3 dtmax = 0.01}
 
    # The CFL tolerance is set to 0.4
    AdvectionParams { cfl = 0.4 }
 
    Global { double interface (double x, double y) {
               return ((y) - 0.4572/0.9144*x);
             }
 
    }
 
    # Initial refinement
    Refine LMIN
    RefineSurface LEVEL (interface(x,y))
 
    # Physical length of a box
    PhysicalParams { L = 5. }  
 
    # Tank bottom
    Solid ((y) - 0.4572/0.9144*(x- 1.0223302793129*2.44/0.4572))
 
    # Fluid
    VariableTracerVOF T
    InitFraction T (interface (x,y))
 
    # We lower the tolerance on the Poisson solver
    ApproxProjectionParams { tolerance = 1e-5 }
    ProjectionParams { tolerance = 1e-5 }
 
    # Definition of functions that read the file containing the time evolution of the position
    # of the solid object and derive the corresponding boundary conditions.
    Global {
	double position (double t) {
             FILE * fin = fopen ("Benchmark_4_run30.txt","r");
             double t0=0, p0=0, t1=0, p1=0;             
 
	     g_assert(fscanf(fin,"%lf %lf\n",&t1,&p1));
 
	     while (t1 <= t) {
		 t0=t1; p0=p1;
		 g_assert(fscanf(fin,"%lf %lf\n",&t1,&p1));
 
		 }
 
             fclose (fin);
 
	     if (t1 == t) {
		 return p1/100;
             }
	     else {
		 return (p0*(t1-t)+p1*(t-t0))/(100*(t1-t0));
             }
        }
 
	double instant_vel (double t) {
             FILE * fin = fopen ("Benchmark_4_run30.txt","r");
             double t0=0, p0=0, t1=0, p1=0;             
 
	     g_assert(fscanf(fin,"%lf %lf\n",&t1,&p1));
 
	     while (t1 <= t) {
		 t0=t1; p0=p1;
		 g_assert(fscanf(fin,"%lf %lf\n",&t1,&p1));
 
		 }
 
             fclose (fin);
 
	      return (p1-p0)/(t1-t0);
	     }
 
	double vel_x (double t, double dt) {
	 if (dt == 0.) 
             return (instant_vel (t));
	 else
             return ((position(t+dt)-position(t))/dt);
	}
    }
 
    # Setup of the moving slide
     SolidMoving liu.gts {
	tx = 0.14142135623731
	ty = 1e-6
	sz = 0.6525
	flip = 1
    } { level = LEVEL }
 
    # 
    SurfaceBc U Dirichlet (vel_x (t, dt))
 
    # Setup of mesh refinement on the solid boundaries
    RefineSolid ( x < 1.5 ? LEVEL : LMIN)   
 
    # Density
    PhysicalParams { alpha = 1./RHO }
 
 
    # Use the reduced gravity approach
    VariablePosition Y T y
    VariablePosition X T x
    SourceTension T -9.81*cos(ANGLE)*(0.01 - 1.) Y
    SourceTension T  9.81*sin(ANGLE)*(0.01 - 1.) X
 
 
    AdaptFunction { istart = 1 istep = 1 } {
 	cmax = 0
        maxlevel = (x < 4. ? LEVEL : LEVEL - 2)
 	minlevel = (T < 1. ? LMIN:0)
    } (T > 0 && T < 1)
 
 
    AdaptVorticity { istep = 1 } {
    	cmax = 1.0
    	maxlevel = LEVEL
        minlevel = LMIN
    }
 
    # Wave gauges
    OutputLocation { istep = 1 } { awk -f distance.awk > probe1 } probe1x { interpolate = 0 }
    OutputLocation { istep = 1 } { awk -f distance.awk > probe2 } probe2x { interpolate = 0 }
    OutputLocation { istep = 1 } { awk -f distance.awk > probe3 } probe3x { interpolate = 0 }
    OutputLocation { istep = 1 } { awk -f distance.awk > probe4 } probe4x { interpolate = 0 }
    OutputLocation { istep = 1 } { awk -f distance.awk > probe4 } probe5x { interpolate = 0 }
 
    # Output control statistics on the simulation
    OutputTime { istep = 1 } stderr
    OutputBalance { istep = 1 } stderr
    OutputProjectionStats { istep = 1 } stderr
 
    # Output simulation files every 0.1 second
    OutputSimulation { step = 0.1 end = 3} sim-%g.gfs
 
    # Viscosity using a fully implicit scheme
    SourceViscosity {} (1./(T/1.78e-5+(1-T)/1.015e-3)) { beta = 1}
 
    # Generates a movie
    GModule gfsview
    OutputView { step = 2e-2 } { ppm2mpeg > movie.mpg } { width = 800 height = 600 } view3D.gfv
 
}
GfsBox {
    left = BoundaryOutflow
    top = BoundaryOutflow
}
GfsBox {
    top = BoundaryOutflow
}
1 2 right

GfsView3D file 'view3D.gfv'

Generated by GfsView


# GfsView 3D
View {
  tx = -0.303493 ty = 0.0588803
  sx = 1 sy = 1 sz = 1
  q0 = -0.175687 q1 = 0.0609815 q2 = 0.294233 q3 = 0.937466
  fov = 4.37797
  r = 0.3 g = 0.4 b = 0.6
  res = 1
  lc = 0.001
  reactivity = 0.1
}
VOF {
  r = 1 g = 1 b = 1
  shading = Constant
  maxlevel = -1
  font_size = 1
  raster_font = 1
} {
  n.x = 0 n.y = 0 n.z = 1
  pos = 0
} P {
  amin = 1
  amax = 1
  cmap = Jet
} T {
  reversed = 1
  use_scalar = 0
  draw_edges = 0
  interpolate = 0
}
Solid {
  r = 1 g = 1 b = 1
  shading = Constant
  maxlevel = -1
  font_size = 1
  raster_font = 1
} {
  n.x = 0 n.y = 0 n.z = 1
  pos = 0
} P {
  amin = 1
  amax = 1
  cmap = Jet
} {
  reversed = 0
  use_scalar = 0
}

Retrieved from "http://gfs.sourceforge.net/wiki/index.php/Liu_et_al_benchmark"

Liu et al benchmark

From Gerris

Revision as of 20:54, 23 March 2011

Contents

Generating the landslide body geometry

Numerical "wave gauge"

3D Results

2D/3D Comparisons

Gerris parameter file 'liu.gfs'

GfsView3D file 'view3D.gfv'

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