Open threads, including the dead ends

In a Godunov scheme the dissipation and the upwinding are one mechanism. In a kinetic scheme they separate, so the dissipative part can be switched on only at the two or three faces straddling the shock — leaving the acoustic feedback path that drives most detonation instabilities essentially inviscid. Its support then shrinks with mesh spacing, and on an unsteady wave this recovers structure normally reported as needing an order of magnitude more resolution.

Because sparse gating needs a non-dissipative branch that does not blow up. With the stabilising term disabled, the kinetic construction stayed stable over long integrations; the conventional analogue failed almost immediately. It earns its place by being shock-stable with dissipation switched off — and is carbuncle-free on unfavourable aspect ratios.

Reference codes still orchestrate regridding and load balancing substantially on the CPU — a round-trip right where the mesh changes fastest. Integer-lattice Morton keys turn the tree into a sorted array, so the whole chain reduces to sorts, scans and scatters with deterministic connectivity. Getting it right on a surface-snapped mesh took three fixes no all-hexahedral test suite can expose.

Operator splitting burns each cell at constant volume, so heat release appears as pressure rather than work — at a reacting front, compounding into a detonation the physics never contained. We use a local coupled update in the spirit of spectral deferred correction: the cell sees its transport contribution while it burns, so it vents. Explicit, local, one correction iteration.

Sensors are either cheap and noisy, or robust and expensive — and the expensive ones introduce stencil-wide reductions into a pass that otherwise maps onto scans. We use the residual between the fluxes assembled on a cell’s faces and the flux its centre state predicts. Every term is already in memory, and it separates discontinuities from smooth flow by several orders of magnitude.

Every mainstream portability layer compiles through a vendor toolchain supporting current accelerators only, excluding the hardware most researchers own. Vulkan with SPIR-V reaches old silicon and is used almost exclusively for machine-learning inference. The solver already runs on GPU through standard C++, chemistry included, bit-identical to the CPU path; the vendor-neutral path is the open work.