Feed a basaltic lava channel at the vent and watch temperature-dependent viscosity, radiative cooling and crust decide how far it runs, then protect the village below.
Missions override the discharge as stated and judge your viscosity, basin and spray settings.
The science
Flow law. For a wide layer of thickness h on slope θ, a Newtonian fluid flows with u = ρ g sinθ h² / (3 μ) (Jeffreys). With a yield stress τy (Bingham) the unit-width flux is q = (ρ g sinθ h³ / 3μ)(1 − 3ξ/2 + ξ³/2), ξ = τy/(ρ g h sinθ); there is no flow when ξ ≥ 1, i.e. when h is below the critical depth hc = τy/(ρ g sinθ).
Temperature dependence. μ(T) = μ₀ exp(b (Tv − T)) with b = 0.023 K⁻¹ (about one decade per 100 K) and τy(T) = τ₀ exp(0.03 (Tv − T)); both are model values of the right order for basalt, not measurements of a particular flow.
Cooling and crust. Each cell cools by radiation and convection: ρ cp h dT/dt = −(ε σ (T⁴ − Ta⁴) + hc(T − Ta))(1 − 0.8 c) with emissivity 0.9, hc = 15 W/m²/K, ρ = 2600 kg/m³, cp = 1200 J/kg/K. The crust fraction c goes from 0 at 1200 K to 1 at 1000 K and insulates the interior.
Numerics. Mass and heat are advected in a 1D finite-volume scheme (upwind, 10 m cells, time step from the kinematic wave speed 3u) along the channel centre-line; bed slope and width come from the terrain. A retention basin keeps lava until its capacity is reached.
Simplifications. One dimension: no lateral spreading, levee building, lava tubes, flow over obstacles, melting of the bed, gas or crystal content. Slope comes from the baked terrain. Educational model; the village is a marker, no one is harmed. Models built with Blender, scene by Three.js.