nx_water_erosion.nx

nx_water_erosion.nx -- full Mei 2007 hydraulic erosion simulation. Mei, Decaudin, Hu 2007: "Fast Hydraulic Erosion Simulation and Visualization on GPU". Full implementation per cardinal `feedback-maximum-capability-no-simplification`: this primitive ships the entire shallow-water + sediment-transport algorithm, not a slope-magnitude approximation. Algorithm (Mei 2007 sections 3.1 - 3.5): STAGE 1 -- WATER INCREMENT (rain) d(t+dt) += dt * r_t where r_t = rain rate per cell STAGE 2 -- FLOW SIMULATION (pipe model) For each cell + each cardinal direction X: f_X(t+dt) = max(0, f_X(t) + dt * A * g * dh_X / L) where dh_X = h(this) + d(this) - h(neighbour_X) - d(neighbour_X), A = pipe cross-section, L = pipe length, g = gravity. Outflow scaling: if total_outflow * dt > available_water * cell_area, scale all 4 outflows by min(1, available_water * cell_area / (total_outflow * dt)). STAGE 3 -- WATER UPDATE (mass conservation) d(t+dt) = d(t) + dt * (total_inflow - total_outflow) / cell_area STAGE 4 -- VELOCITY FIELD delta_W_x = (f_R(left_neighbour) - f_L(this) + f_R(this) - f_L(right_neighbour)) / 2 u = delta_W_x / (cell_size * d_avg) (similar for v, y axis) STAGE 5 -- EROSION + DEPOSITION C = K_c * |sin(local_tilt)| * |velocity| (sediment capacity) if C > s: erode -> h -= K_s * (C - s); s += K_s * (C - s) if C < s: deposit -> h += K_d * (s - C); s -= K_d * (s - C) STAGE 6 -- SEDIMENT TRANSPORT (semi-Lagrangian) s_new(x, y) = s_old(x - u*dt, y - v*dt) -- bilinear interp STAGE 7 -- EVAPORATION d(t+dt) = d(t) * (1 - K_e * dt)