Illustration of the sweep substepping procedure. The rectangles represent cells, with the color of the cell indicating how far the cell has been integrated. A fully blue cell has not been integrated at all, while a green cell has been integrated for a total of Δt_max. Arrows represent fluxes going into the cell which are computed during the sweep steps. Black arrows denote normal fluxes, while orange arrows represent boundary terms for the sweep. Each row represents either a sweep (denoted by S) or a chemistry update (denoted by C) at the corresponding level l. The last row represents the final state with each cell having been fully integrated.