Monte Carlo simulation of low density flows

The necessity for adopting a kinetic-theoretical approach to obtain aerodynamic characteristics in low density flow past space vehicles is highlighted in this paper; it is shown how long-standing difficulties in theoretically handling such flows can be circumvented by adopting a Monte Carlo technique. The principles underlying the technique are briefly described, and are first illustrated by applying the technique to the evaluation of the drag of cylinders and cones in collisionless flow. The Markoff process underlying the Monte Carlo simulation of the full Boltzmann equation with collisions is then described in detail. Instead of the time-counter strategy of Bird, a theoretically sounder ‘Random Collision Number’ (RCN) strategy has been adopted in the present simulation. In this strategy the number of collisions in each time-step in the computation is a random number drawn from an appropriate distribution. Computer programs using this strategy have been developed for calculating aerodynamic characteristics like drag and heat transfer for a cone in the transition regime between free molecule and continuum flow. The results obtained from these programs show that both time-counter and RCN strategies require almost the same computer time.