When a gas is dense, continuum fluid dynamics (the Navier-Stokes equations) works well because molecules collide with each other far more often than they travel any appreciable distance. But in rarefied conditions — high-altitude re-entry vehicles, vacuum chambers, micro/nano-scale flows — the gas becomes so thin that molecules can travel a long way between collisions. Continuum assumptions break down, and the flow must be modelled molecule-by-molecule.
Direct Simulation Monte Carlo (DSMC), developed by Graeme Bird in the 1960s, is the standard technique for this regime. Instead of tracking every real molecule (there are far too many), DSMC tracks a much smaller number of representative simulator particles that move ballistically and undergo collisions chosen probabilistically, statistically reproducing the true collision rate.
DSMC is exactly the technique NASA uses to predict heating and drag on spacecraft during the rarefied upper-atmosphere phase of re-entry, before the air is dense enough for ordinary computational fluid dynamics to apply.
Watch a molecular gas stream past a plate and see how the Knudsen number determines whether it behaves like a smooth continuum fluid or a spray of independently colliding particles, using a Direct Simulation Monte Carlo collision model.
Particles are grid-binned into cells each frame and stochastically paired for probabilistic collisions — the core DSMC move — with pairing probability falling as Knudsen number rises, reproducing the transition from continuum to free-molecular flow.
Drag the Knudsen number slider from dense (continuum) to rarefied (free-molecular) and watch the flow regime badge and deflection pattern change. Adjust particle count and stream speed, and toggle collision flashes and velocity streaks.
NASA uses DSMC, developed by Graeme Bird, to predict aerodynamic heating and drag on spacecraft in the thin upper atmosphere during the rarefied phase of re-entry, before ordinary CFD becomes valid.