Model QC

The Check That Saves the Run

A finite-difference simulation can cost hours of compute. The cheapest possible mistake is launching one on a model that was never going to work, a grid too coarse or a time step too large. This closing section is the preflight checklist that catches those failures in a millisecond instead of at hour three, and it turns three numerical rules from earlier in the course into a go or no-go decision.

The velocity range comes first, because the fastest and slowest velocities set every other limit. Then the CFL stability condition from Part 4: the time step must be small enough that a wave cannot cross more than a fraction of a grid cell per step, or the scheme amplifies every step until it overflows. Then numerical dispersion: the grid must sample the shortest wavelength with enough points, or the wave scatters off the numerical grid itself and arrives mis-timed.

Green Light or Wasted Compute

Move the grid spacing, the time step, and the maximum frequency, and watch each check flip between pass and fail. Raise the time step past the CFL limit and the Courant number climbs above one, the red condition that guarantees a blow-up. Coarsen the grid and the points per wavelength fall below five or six, the point where dispersion sets in. The whole model is ready only when all three pass with margin.

This is fit-for-purpose thinking taken to its natural end. A model is not finished when it looks right on screen; it is finished when it will run correctly on the engine you intend to use. That is the discipline the whole course has taught, from choosing convolution over the wave equation, to choosing acoustic over elastic, to choosing a resolution and a format. Everything now assembles into the final part: the Modeling Lab, where you build, run, view, and export a synthetic in one workbench, and then take the physics to real research tools.