Fuel-Consumption

Fuel fraction remaining and burning area fraction of one fire-grid cell as computed by fire_behavior's Calc_fuel_left (physics/level_set_mod.F90): the cell is split into a 2x2 submesh (fuel_left_irl = fuel_left_jrl = 2); at the four corners of every subcell the level-set function and the ignition time are bilinearly interpolated from the 3x3 node neighbourhood of the cell (the node values are the cell-centred lfn and tign_g of the cell and its eight neighbours; subcell (1,1) uses nodes (i-1..i, j-1..j) at fractions 1/2..1, subcell (2,1) nodes (i..i+1, j-1..j) at fractions 0..1/2 and so on); each subcell's burning area is the level-set sign fraction (1 - sum lfn/sum|lfn|)/2 (Mandel et al. 2011 Sect. 3.2) and its remaining fuel is area exp(-(time_now - tign_mean)/fuel_time) + (1 - area) with the mean of the four corner times since ignition (zero for unburnt or not-yet-ignited corners); the cell values are the subcell means. The per-step burnt fraction fuel_frac_before - fuel_frac feeds Calc_fire_fluxes. For a cell that is entirely burning with uniform ignition time this is the exact solution of dF/dt = -F/fuel_time (EarthSciModels level_set/fuel_consumption.esm, Mandel eq. 3), exposed as dfuel_frac_dt_burning; for partly burning cells the subgrid integration has no single-ODE equivalent, which is why this component is transcribed rather than reusing FuelConsumption. Tests: cells of the instrumented test7 run at step 20 (real32), rel 1e-5 (abs 1e-7 where a subcell fraction is exactly 0 or 1).