Safety-critical
When does a flame become a detonation?
A flame in confinement accelerates, compresses the gas ahead of it, and past some threshold that compression ignites and the whole thing transitions — with overpressures far beyond what the deflagration could produce. Whether it happens in a given geometry is the question industry most often has to answer with a correlation.
FigureAdaptive refinement following a moving front, with the level jump between neighbouring cells constrained. A schematic of the mechanism.
Why it is hard
Small errors on either side of the flame–flow coupling move the threshold, and the threshold is the quantity of engineering interest. It is also the most unforgiving test of a reactive scheme we know: operator splitting, interpolation at a refined front, a low-dissipation flux at a thermal contact — each has a failure mode that produces a transition the physics never contained. A predicted detonation is only useful if you can rule out the numerical ones.
How we attack it
Attack the known artefacts individually and prove each is gone, rather than tuning a case until it looks right. We have traced several apparent physical results in our own work back to the method, the initial condition and the mesh. And we hold a hard line against case-specific fixes: no forced refinement where we expect the front, no sensor clipped where we have already decided the flow is smooth. Those make the picture better and the prediction worthless.
What we have established
- Several classes of spurious transition come from identifiable, removable defects in the method rather than from physics.
- The choice of energy variable decides whether refinement can manufacture heat at a front — a modelling decision, not an implementation detail.
- An initial condition can contain the event you are trying to predict. We have caught this in our own setup more than once.