From Gerris
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Revision as of 01:40, 29 March 2011
This benchmark for simulations of landslide tsunamis generated by a deformable slide using Gerris is based on these articles:
Zweifel, A., Zuccala, D., Gatti, D.  Comparison between computed and experimentally generated impulse waves
 Journal of Hydraulic Engineering 133(2):208216, 2007
 Bibtex
Cremonesi, M., Frangi, A., Perego, U.  A Lagrangian finite element approach for the simulation of waterwaves induced by landslides
 Computers and Structures In press, 2011
 Bibtex
Here the slide is modeled as a Bingham fluid. The setup is well described in (Cremonesi et al., 2011) except for the initial position of the slide that I could not find in the papers. Fortunately, I managed to digitize the initial position of the slide from Figure 101 and 111 of (Cremonesi et al., 2011).
Two configurations are tested here. First the case of a slide with no initial velocity (initial x coordinate of the leading edge of the slide = 0.5 m with respect to the shoreline), and then that of a slide with an initial velocity of 3.153 m/s (initial x coordinate of the leading edge of the slide = 0.84 m with respect to the shoreline).
The experiments are quasi twodimensional and therefore as (Cremonesi et al., 2011) we start by doing the twodimensional simulations.
Results
Those are preliminary results obtained using the viscosity and yield stress that (Cremonesi et al., 2011) had to use so that their Bingham fluid would collide into the water at the same velocity as that recorded in the experiments.
The results are not impressive with both amplitude and timing significantly wrong.
Evolution in time of the VOF interface for a simulation with adaptive refinement down to level 8

Simulation file
# Maximum resolution Define LEVEL 6 # Minimum background resolution Define LMIN 2 # Initial velocity of the slide Define U0 3.153 # Distance between the leading edge of the slide and the shoreline Define X0 0.84 # Bingham fluid Define MODEL 3 13 17 GfsSimulationMoving GfsBox GfsGEdge { x = 0.2 y = 0.2 } { # Sets the duration of the simulation to 3 time units Time { end = 4 dtmax = 0.01} # We force the timestep to be as low as 0.005 for the first 5 timesteps Event { step = 0.00001 iend = 5 } # The CFL tolerance is set to 0.4 AdvectionParams { cfl = 0.4 } Global { #define r_w 1000.0 /* Density of water */ #define r_a 10.0 /* Density of air */ #define r_s 1500.0 /* Density of solid */ #define mu_w 0.0001 /* viscosity of water */ #define mu_a 0.0000178 /* viscosity of air */ #define mu_l 75. /* viscosity of liquid slide */ #define mu_s 1000. /* viscosity of solid slide */ double slide (double x, double y, double z) { return MIN(MIN((y  (x + 2.*X0+sqrt(2.)*0.6 )), (y  (x + 2.*X0))),(y + (x  sqrt(2)*0.236))); } double RHO (double tw, double ts) { return 1./(ts*1./r_s+(1.ts)*((1tw)*1./r_w + tw*1./r_a)); } double MU (double tw, double ts, double d2) { double ty = 35.; double m, mu, N; switch (MODEL) { case 0: /* Newtonian */ ty = 0.; N = 1.; break; case 1: /* Powerlaw (shearthinning) */ ty = 0.; N = 0.5; break; case 2: /* HerschelBulkley */ N = 0.5; break; case 3: /* Bingham */ N = 1.; break; } if (d2 > 0.) m = ty/(2.*d2) + mu_l*exp ((N  1.)*log (d2)); else { if (ty > 0.  N < 1.) m = mu_s; else m = N == 1. ? mu_l : 0.; } mu = MIN (m, mu_s); return 1./(ts*1./mu+(1.ts)*((1tw)*1./mu_w + tw*1./mu_a)); } } # Physical length of a box PhysicalParams { L = 1. } # Slope Solid (y + x) # Air/Water VOF tracer VariableTracerVOF T # Slide VOF tracer VariableTracerVOF TS # Initial air/water interface InitFraction T (y) # Initial slide position InitFraction TS (slide(x,y,z)) # Sets initial slope, air/water interface and slope refinement RefineSolid LEVEL RefineSurface { return x > 1. ? LEVEL : LMIN;} (y) RefineSurface LEVEL (slide(x,y,z)) # We lower the tolerance on the Poisson solver ApproxProjectionParams { tolerance = 1e5 } ProjectionParams { tolerance = 1e5 } # Sets the initial velocity of the slide Init { } { U = (TS*U0/sqrt(2.)) V = (TS*U0/sqrt(2.)) } # Density PhysicalParams { alpha = 1./RHO(T,TS) } # The osition of the VOF interface is stored in X and Y VariablePosition Y T y VariablePosition X T x # Gravity Source {} V 9.81 Init { istep = 1 } { SEB = MU(T, TS, D2) } # Refinement if the air water interface AdaptFunction { istart = 1 istep = 1 } { cmax = 0 maxlevel = (x < 4 ? LEVEL : LEVEL  2) minlevel = (T < 1. ? LMIN:0) } (T > 0 && T < 1) # High refinement inside the slide AdaptFunction { istart = 1 istep = 1 } { cmax = 0 maxlevel = (LEVEL  1) } ( TS ) # Refinement of the slide's interface AdaptFunction { istart = 1 istep = 1 } { cmax = 0 maxlevel = (x < 4 ? LEVEL : LEVEL  2) minlevel = (T < 1. ? LMIN:0) } (TS > 0 && TS < 1) # Refinement using the vorticity criterion 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 } # Output control statistics on the simulation OutputTime { istep = 1 } stderr OutputBalance { istep = 1 } stderr OutputProjectionStats { istep = 1 } stderr # Output simulation files every 0.1 s OutputSimulation { step = 0.1 end = 3} sim%g.gfs OutputSimulation { step = 0.5 start = 1.5} sim%g.gfs # Viscosity of the fluids SourceViscosity {} (MU(T,TS,D2)) { beta = 1 } # Generates a movie GModule gfsview OutputView { step = 2e2 } { ppm2mpeg > movie.mpg } { width = 800 height = 600 } view2D.gfv } GfsBox { bottom = Boundary { BcDirichlet U 0 } } GfsBox { bottom = Boundary { BcDirichlet U 0 } } GfsBox { bottom = Boundary { BcDirichlet U 0 } } GfsBox { bottom = Boundary { BcDirichlet U 0 } } GfsBox { bottom = Boundary { BcDirichlet U 0 } } GfsBox { bottom = Boundary { BcDirichlet U 0 } } GfsBox { top = BoundaryOutflow } GfsBox { top = BoundaryOutflow } GfsBox { top = BoundaryOutflow } GfsBox { top = BoundaryOutflow } GfsBox { top = BoundaryOutflow } GfsBox { top = BoundaryOutflow } GfsBox { top = BoundaryOutflow } 1 2 right 2 3 right 3 4 right 4 5 right 5 6 right 7 8 right 8 9 right 9 10 right 10 11 right 11 12 right 1 7 top 2 8 top 3 9 top 4 10 top 5 11 top 6 12 top 7 13 left
