Modeling of Rock Slide Impact into Water

Transcription

1 Modeling of Rock Slide Impact into Water Galen Gisler Physics of Geological Processes University of Oslo Åknes/Tafjord Workshop, 30 August

2 Background on the Sage code Need for compressible hydrodynamics Equation of State Preliminary Åknes rock slide simulations Initial conditions - inputs to Sage from rock dynamics Problems with initialization in three dimensions Trial runs in two dimensions Wave heights and energies Preparing for three dimensional run 2

3 Sage is a multi-phase compressible hydrodynamics code. Joint development SAIC & Los Alamos Eulerian, cell-by-cell adaptive mesh refinement Multi-material, multi-phase, compressible Godunov, 2 nd order alternating direction explicit Tabular or analytic equations of state Rigorous verification and validation Example frame from Sedov verification problem 3

4 Why compressible hydrodynamics? Water is nearly incompressible, so is rock, but the two have very different acoustic speeds. So there will be heating and energy dissipation. With very energetic interactions, heating will produce compressible effects. Violent interaction of rock with water produces shocks and cavitation vortices. Phase changes may occur; fragmentation will occur. 4

5 The fundamental equations of hydrodynamics are conservation laws. Continuity: ρ t + ρ u ( ) = 0 Momentum: ρ u t + ( ρu u ) + σ = 0 Total Energy: ρe t + ( ρue ) + ( σ u ) + q = 0 For completeness you need a constitutive relation σ = F ρ, E,history, ( ) 5

6 SAGE has a good tabular equation of state for water. This is the SAIC equation of state for water, incorporated into Sage. Lines are observed phase stability lines, and color represents density returned by the table in Sage. Physics includes latent heats at phase changes; energy conservation is important! Tables for some other materials of interest are available from the LANL Sesame database. 6

7 One of our validation examples was the Lituya Bay event. On 1958 July 8, a landslide generated a tsunami with a 524-meter run-up on the opposite side of the bay. This was modeled in lab experiment at 1:675 scale by Hermann Fritz, ETH Zürich. Charles Mader simulated lab experiment and real tsunami using SAGE (2001). 7

8 Sage reproduced both the experiment and the real event. Photos and particle velocimetry courtesy of Hermann Fritz Simulation by Charles Mader The extent of run-up and the reported time to maximum run-up were well replicated in both experiment and simulation. 8

9 Sage has been used in a variety of tsunami simulations since then. Asteroid impacts Underwater explosive volcanic eruptions La Palma flank collapse scenario Underwater landslides 9

10 Our preliminary Åknes simulations We took the S2 model from Preh et al, with positions of 2543 boulders at first impact. We attempted to initialize a three-dimensional run, but code errors prevented the grid from being generated. In two-dimensions, we succeeding in generating a grid if we eliminated just one boulder. We ran this case and two limiting schematic cases. Slope continues into deep water; no other fjord geometry included. 10

11 2-D run with hard boulders Boulders, distinct in 3-D, overlap and fuse in 2-D. Rock assembly overturns, causes second pulse. 11

12 2-d thin fluid wedge, rock density Thin fluid wedge drives a surprisingly big wave. Interchange instability causes second pulse. 12

13 2-d thick fluid wedge, rock density Wedge front drives tall splash. Two-fluid instabilities cause turbidity currents 13

14 Wave heights in the 2-D runs are high wave height (m) 150 distance (m) boulders 50 Boulders thin fluid wedge 500 thin fluid wedge thick fluid wedge thick fluid wedge distance (m) time (s) Constant wave height is rapidly achieved in all cases. All runs show acceleration as wave moves into deeper water. Average speed is 40 m/s. 14

15 Most of the energy goes into heat. Energy, ergs kinetic energy water kinetic energy boulders potential energy boulders internal energy boulders Overall efficiency of tsunami generation is ~12.5%. Heating rock takes up ~32.9% Rest goes into heating water and air time, seconds 15

16 We intend to do 3-D runs next. We ve identified and fixed the grid generation problem. We need a CAD model of the fjord topgraphy/ bathymetry. The runs will require approximately cpu hours each. Computer time may be available at the Alaska Regional Supercomputing Center. 16