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. jmelosh_at_lpl.arizona.
  edu).

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Why Create Computer Models?

• Expand (contract) size scale from experimentally
  feasible studies
• Study conditions beyond the reach of experiment
  (eg. velocity)
• Verify the physics

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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!

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BEWARE!

• Just because a computer image looks good, doesnt
  mean it represents reality!

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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
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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

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Imagine a complex geologic system
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Divide it into smaller elements
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The number of elements depends on the desired
resolution and the number of space dimensions
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• 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

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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).

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The amount of computer storage needed depends on
the desired resolution--you cannot simulate a
planet and a rock in the same calculation!
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• The runtime required for a computation depends on
  the model duration, T, and the resolution r
• Stability requires that the time step Dt be a
  fraction (usually about 1/5) of the time for
  sound to traverse the smallest cell
• Dt r/soundspeed
• The number of timesteps is T/ Dt
• So the total runtime is proportional to N times
  the number of cells in the model

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For the same example as before, assuming the
computation takes 1 ms/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

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The first 2-D simulation of an impact (Bjork et
al 1967) proudly displayed the resolution
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Most modern simulations dont
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But it is there, and resolution tests for
accuracy should be made for every simulation
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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!

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• There are two basic types of hydrocode
  simulations, each with its own advantages and
  drawbacks

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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

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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

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Hydrocode modeling stands on two main pillars
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Equations of State

• Perfect Gas
• Stiffened Gas
• Grüneisen
• Tillotson
• ANEOS
• SESAME
• ???

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Constitutive Relations

• Elasticity
• Viscosity
• Strength
• Fracture mechanics, tensional and compressional
• Porosity/dilatency
• How to treat mixed materials in Eulerian
  simulations?

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The Pacific Craters Problem

• A thrilling tale of Simulation vs. Observation,
• Courtesy of DoD turf wars

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Nuclear testing on Enewetak Atoll in 1958
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Produced some remarkable craters
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Broad and Shallow, no simulation succeeded in
modeling them!
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The Moral

• Observation, Experiments and Modeling cannot be
  successful by themselves
• Communication between all three disciplines is
  essential!

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• Happy Birthday, Zibbi!