03 / Coupling · ownership and timing

Follow an exchange all the way back

A reaction must reach the other solver. Compare the impulse waiting in its accumulator with the state after it has been consumed.

SPH mass / heat capacityMPM mass / heat capacityExchange progress

In the momentum view, the SPH side changes first and the reaction stays in a persistent accumulator. MPM consumes that impulse as Δv = J/m, then clears it. In the heat view, both participants approach the same capacity-weighted temperature.

—Before exchange

—After / stored

—Ledger error

Equations and model boundary

J = −(vₐ − vᵦ)/(1/mₐ + 1/mᵦ)
Tₘᵢₓ = (CₐTₐ + CᵦTᵦ)/(Cₐ + Cᵦ)

The contact impulse is an ideal inelastic two-body example, not the native SPH contact law. The ledger illustrates the native store/consume ordering. Heat uses the exact exponential solution of equal-rate relaxation (rate 0.45); the native path uses explicit steps and spatial scatter/gather, so the ideal conservation shown here does not establish whole-solver conservation.