Multiscale physics
How much of a reaction zone must you actually resolve?
Reactive flow spans microns inside metres. The standard answer is to resolve everything, which is why this class of problem is associated with national-laboratory machines. We are interested in the narrower question: what has to be resolved, and what merely appears to.
FigureThe transverse structure a propagating reaction front develops as it becomes unstable. A schematic of the mechanism, not a computed field.
Why it is hard
Stiff source terms do not degrade gracefully. An under-resolved reaction zone gives you the wrong propagation speed, and in the worst case a wave that was never in the physics. That makes the usual engineering instinct — coarsen until affordable, then check convergence — actively dangerous, because a coarse computation can be smooth, stable, converged-looking and wrong.
How we attack it
Treat resolution as a question rather than a budget. We characterise what a scheme does to the relevant physics as the mesh coarsens, using observables that are sensitive to it instead of error norms that are not. Then we attack the requirement directly: reduce what the method destroys, so the mesh only has to resolve the physics rather than compensate for the scheme.
What we have established
- A substantial part of what is normally blamed on resolution belongs to the method instead, and is recoverable.
- Dynamical observables detect under-resolution far better than convergence in a norm.
- Coarse-mesh agreement that survives a change of method is meaningful. Agreement that does not is a coincidence.