Navier-Stokes Simulations of Surface Waves Generated by ...

Navier-Stokes Simulations
of Surface Waves Generated
by Submarine Landslides:
Effect of Slide Geometry
and Turbulence
D. Basu, S. Green, K. Das, R. Janetzke,
J. Stamatakos
Southwest Research Institute®, 6220 Culebra Road, San
Antonio, TX 78238, USA
2009 SPE Americas E&P Environmental & Safety
Conference
San Antonio, Texas, USA, 23–25 March 2009

Outline of Presentation
•Background
•Objectives
•Technical approach
•Results
•Conclusions

Background
Tsunami science has evolved significantly over
the last few decades
Important class of natural hazards
Most commonly triggered by large-magnitude submarine earthquakes
Active research in submarine landslide generated
tsunamis
Primarily occurs in world’s oceans
Locally Intense and Potentially Destructive
Large run-ups Damage coastlines
Affects the off-shore oil and gas industries
Increased use of computational fluid dynamics
(CFD) in tsunami modelling
Full Navier-Stokes Equations
Faster processors
Better and faster numerical schemes : both spatial and temporal
Advanced grid generation techniques to deal with complex geometries

Significance of Research
•Efficient computational tool for prediction of landslide
generated tsunami :
•Oil and Gas Industry
•Oil exploration region
•An increasing proportion of the world’s oil and gas is now
recovered from deepwater areas offshore
•Landslide-generated tsunamis can present significant
risks to offshore structures, such as oil and gas production
platforms and remote terminal facilities
•Turbulence, three-dimensionality in models, and landslide
shape influence the generated tsunami waves

Landslides Generated tsunami
Landslide

Existing Numerical Models
Techniques Used Commonly for tsunami models :
• Shallow water equations
– Depth Averaging
• Fully Non-Linear Potential Flow (FNPF) Model
– Laplace’s Equation Boundary Integral Equation Boundary Element
Method
• Linear Theory Simulations
– Seafloor Uplift + Simple and Complex Slide
– Green Function’s Approach
• Water wave propagation Equation
– 2-D Euler equations for mass and momentum (N-S equations with
viscosity neglected)
• EACH OF THESE METHODS HAVE BEEN USED IN EARTHQUAKE
GENERATED TSUNAMI MODELLING
Computational Method for simulating landslide generated tsunami
waves : Navier-Stokes Equations with Free Surface Tracking
Algorithm [Volume of Flow (VOF)] Method.

Objectives
•Numerically simulate landslide generated
tsunami wave : Compare simulated results
with experimental data
•Analyze the effect of slide geometry on the
impulse wave characteristics and run-up
•Assess the effect of turbulence model &
computational grid on the predicted wave and
run-up
•Evaluate three-dimensionality of the flowfield

Technical Approach Solver
•Navier-Stokes Volume of Flow (VOF) Approach with FLOW-
3D
•FLOW-3D : (Flow-Sciences Inc.)
•Solves full Navier-Stokes equations
•Employs volume of flow (VOF) method by FAVOR
(Fractional area volume representation) technique
•Number of turbulence models including RNG k-є models
and LES models
•Includes two fluid drift flux model as approximate Eulerian-
Eulerian formulation

FLOW-3D
Developer: Flow Sciences Inc
Finite difference method
OpenMP and MPI based Parallelization
Multi-block structured grid
Flow-3D®
Different turbulence models
Post-processor FLOWVU and FLOWPLOT
Customization

Current Simulations
•Experimental data of Heinrich (1992)
•Spatial Discretization : Implicit Scheme
•Temporal Discretization : Semi-Implicit Scheme
•FAVOR defines solid boundaries within the Eulerian grid
•Two Turbulence Models used in the current analysis :
–RNG Turbulence model (k-ε based) (Pure RANS model)
–Detached Eddy Simulation (DES) based multiscale model
–Both these models solve the equations for turbulent kinetic energy (k)
and the turbulent kinetic energy dissipation rate (ε)
•One case with laminar flow also simulated
•Unsteady simulations
•Landslide was represented by solid sliding wedges
•Three slide geometries were used
•Mass of the slide was kept constant

DES Multiscale Model
•The DES modeling approach differs from the RANS modeling approach by
the eddy diffusivity closure through a switching function
•The DES formulations allow the reduction of eddy viscosity in the regions of
interest, and fine scales are resolved.
•A switching function is used to activate the reduction in eddy viscosity.
•The DES model was incorporated in the FLOW-3D solver
RANS
model
Multiscale DES
model
RANS
Model
Reduction in Eddy
Diffusivity
RANS
Model
Reduction in Eddy
Diffusivity
RANS
Model
Reduction in Eddy
Diffusivity

Geometry & Parameters
•The experiments were carried out in a
channel 20-m long, 0.55 m wide, and 1.50 m
deep in the Hydraulic National Laboratory,
Chatou, France
•The sliding wedge has a density of 2000
kg/m 3 , and 45 o incline
•The wedge velocity profile is given by
V(t)=86 tanh(0.0175t), t ≤ 0.4s (1)
V(t)=0.6 t > 0.4s
(2)
Wedge Velocity m/s
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 0.5 1 1.5 2
Time s

Geometry & Parameters (Contd.)
•Three geometrical shapes for the slide were considered :
•Triangular Geometry
•Elliptical geometry
•Rectangular Geometry
•Computational grid used in the Analysis
Baseline Grid : 120×40×40 cells in the x-, y-, and z-directions
Coarser Grid : Resolution 1.414 times the baseline grid
Finer Grid : Resolution 0.707 times the baseline grid
•Effect of DES model constant C b on the analysis : Three
different values of C b were used (C b = 0.1, 0.3, 0.5)

GENERAL FLOWFIELD
(MOVIE-2D)

GENERAL FLOWFIELD
(MOVIE-3D)

TIME DEPENDENT FLOW-FIELD
Dynamic Viscosity Pa*sec
Dynamic Viscosity Pa*sec
1.20 m
1.20 m
4.10 m
4.10 m
T = 0.5 secs
T = 1.0 secs
Dynamic Viscosity Pa*sec
1.20 m
Simulations carried out
using multiscale DES
model and with C b
= 0.3
4.10 m
T = 1.5 secs

Effect of Slide Geometry (RANS model)
Rectangular Slide
Elliptical Slide
Simulations carried out
using RNG k-ε RANS
model
Triangular Wedge Slide

Effect of Slide Geometry (DES Model)
Dynamic Viscosity Pa*sec
Dynamic Viscosity Pa*sec
1.20 m
1.20 m
4.10 m
Rectangular Slide
4.10 m
Elliptical Slide
Dynamic Viscosity Pa*sec
1.20 m
Simulations carried out
using multiscale DES
model and with C b
= 0.3
4.10 m
Triangular Wedge Slide

RANS & DES comparison
Dynamic Viscosity Pa*sec
1.20 m
4.10 m
DES Multiscale Model C b
= 0.1
DES Multiscale Model C b
= 0.3
DES Multiscale Model C b
= 0.5
RANS Turbulence Model

1.10
Fluid Surface Height
& Wave Run-up
1.05
Surfqace Height m
1.00
0.95
0.90
0.85
0.80
0.75
0.70
Time = 1 s after Block Release
2-D Laminar
2-D Experiment (Heinrich)
3D Rect, Cb=0.3
3D Ellipse, Cb=0.3
3D, Wedge, Cb=0.1
3D, Wedge, Cb=0.3
3D, Wedge, Cb=0.3, Fine
3D, Wedge, Cb=0.3, Coarse
3D, Wedge, Cb=0.5
0.0 1.0 2.0 3.0 4.0
Position from 'Shoreline' m
Surface Height (m)
Wave Runup m
0.10
0.05
0.00
-0.05
2D Laminar
Wedge, MST, Cb=0.1
-0.10
Wedge, MST, Cb=0.3
Wedge, MST, Cb=0.5
-0.15
Wedge, MST, Cb=0.3, Coarse
Wedge, MST, Cb=0.3, Fine
Wedge, RNG
-0.20
Rectangle, MST, Cb=0.3
Ellipse, MST, Cb=0.3
-0.25
0.0 0.5 1.0 1.5 2.0
Time after Block Release s
Wave Runup (m)

Three-dimensionality
of the flow-field
Isosurface of Q=0.2
Side Structures
Front Edge Structure
Ramp
Wedge

Conclusions
•Flow is strongly three-dimensional and turbulent
•Slides with hydrodynamically efficient shapes produce less turbulence and
bluff body effect
•The flow turbulence is found to be localized
•Flow turbulence do not greatly affect the far field effects such as wave height and
runup
•In the near field, however, turbulence appears to play a stronger role
•Multiscale DES models result in less diffusive solution compared to RANS
model. Diffusivity can be controlled by the parameter C b
•Computational grids do not have any significant influence on the predicted
wave runup or surface height.
•CFD based computational tool can help provide inputs to assess risk from
landslide-generated tsunamis for near shore as well as offshore structures

Acknowledgements
•Advisory Committee for Research at the
Southwest Research Institute
• Technical support staff from Flow-
Sciences, Inc