Moving-interface conservation jump identity
= Moving-interface conservation jump identity
{title2=$\partial_ta+\nabla\cdot b=([b]\cdot n-v_n[a])\delta_s$}
For a moving level surface, $n=\nabla S/|\nabla S|$, $v_n=-S_t/|\nabla S|$, and the <surface delta distribution> is $\delta_s=|\nabla S|\delta(S)$. Piecewise classical conservation laws acquire a distributional flux defect $[b]\cdot n-v_n[a]$. Vanishing of this defect is the <Rankine-Hugoniot condition>.