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

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 ~N 2 For a 3-D simulation, storage ~N 3

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!