modeling meteorite impacts what we know and what we would like to know
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MODELING METEORITE IMPACTS WHAT WE KNOW AND WHAT WE WOULD LIKE TO KNOW. H. J. Melosh (Lunar and Planetary Lab, University of Arizona, Tucson AZ 85721. [email protected]). Why Create Computer Models?. Expand (contract) size scale from experimentally feasible studies - PowerPoint PPT PresentationTRANSCRIPT
MODELING METEORITE IMPACTS
WHAT WE KNOW AND WHAT WE WOULD LIKE TO KNOW
H. J. Melosh (Lunar and Planetary Lab, University of Arizona, Tucson
AZ 85721. [email protected]).
Why Create Computer Models?
• Expand (contract) size scale from experimentally feasible studies
• Study conditions beyond the reach of experiment (eg. velocity)
• Verify the physics
Models must be tested!
• Models of experiments are important
• Models must be compared with observations
• Lessons from DoD code verification program--Pacific Craters debacle not all bad!
BEWARE!
Just because a computer image looks good, doesn’t mean it represents reality!
Decide what you want to know
Are we modeling a Planet? Or a Rock?
You must decide on a scale, L, before you can start a modeling task
Resolution, r
All models work by discretizing a real object into a large number of smaller elements (cells) whose properties and interactions with neighbors are represented by averages
Imagine a complex geologic system
Divide it into smaller elements
The number of elements depends on the desired resolution and the number of space
dimensions
The number of cells translates into the amount of memory a computer must have to do the simulation:
• For a 1-D simulation, storage ~ N
• For a 2-D simulation, storage ~N2
• For a 3-D simulation, storage ~N3
For example, assuming a small problem in which 10 double-precision numbers are stored
for each cell (80 Bytes/cell) and N = 1000,
• For 1-D, need 80 kBytes storage (trivial!)
• For 2-D, need 80 MBytes storage (This labtop can do that easily!)
• For 3-D, need 80 GBytes storage (now we are up to supercomputers).
The amount of computer storage needed depends on the desired
resolution--you cannot simulate a planet and a rock in the same
calculation!
The runtime required for a computation depends on the model duration, T, and the resolution r:
Stability requires that the time step t be a fraction (usually about 1/5) of the time for sound to traverse the smallest cell:
t = r/soundspeed
The number of timesteps is T/ t
So the total runtime is proportional to N times the
number of cells in the model
For the same example as before, assuming the computation takes 1 s/cell, to get to the time
for sound to traverse the entire mesh
• For 1-D, need 5 million operations, or 5 sec of runtime
• For 2-D, need 5 billion operations, or 1 hour of runtime
• For 3-D, need 5 trillion operations, or 1 month of runtime
The first 2-D simulation of an impact (Bjork et al 1967) proudly displayed the resolution
Most modern simulations don’t
But it is there, and resolution tests for accuracy should be made for every simulation
What “test” means…
Is that the result important to you (whether it be mass of rock melted, maximum shock pressure, speed of ejecta, etc.
Must NOT depend on the resolution, r!
There are two basic types of hydrocode simulations, each with its own advantages and
drawbacks:
Lagrangian
• The cells follow the material--the mesh itself moves
• Free surfaces and interfaces are well defined
• But mesh distortion can end the simulation too soon
Eulerian
• Material flows through a static mesh
• Material interfaces are blurred
• Cells contain mixtures of material
• Mesh must be large enough to contain entire time evolution
Hydrocode modeling stands on two main pillars:
Equations of State:
• Perfect Gas
• Stiffened Gas
• Grüneisen
• Tillotson
• ANEOS
• SESAME
• ???
Constitutive Relations:
• Elasticity• Viscosity• Strength• Fracture mechanics, tensional and
compressional• Porosity/dilatency• How to treat mixed materials in
Eulerian simulations?
The Pacific Craters “Problem”
A thrilling tale of Simulation vs. Observation,
Courtesy of DoD turf wars
Nuclear testing on Enewetak Atoll in 1958
Produced some remarkable craters
Broad and Shallow, no simulation succeeded in modeling them!
The Moral:
Observation, Experiments and Modeling cannot be successful by
themselves:
Communication between all three disciplines is essential!
• Happy Birthday, Zibbi!