Analyses of numerical errors in the kinetic modeling of microthruster devices

A comprehensive numerical analysis of a three-dimensional microelectromechanical system-based micro-propulsion system has been performed using the direct simulation Monte Carlo method. The transitional flow regime in the viscous nozzle flow prevents the use of Navier-Stokes based approaches, but the flow is still computationally difficult for the direct simulation Monte Carlo method. The numerical aspects of the direct simulation Monte Carlo approach are sufficiently challenging such that the traditional manner of establishing numerical convergence by observing the lack of change in the solution for increased numbers of computational particles and cells, even for a computation of 130 × 10⁶ particles, fails. Therefore to obtain confidence in the presented results, a better understanding of the nature of the computational errors is necessary. The statistical and deterministic error analyses provided in this article allow us to support the validity of the presented results for low stagnation pressure microelectromechanical system micronozzle flows as well as to suggest a procedure for evaluating numerical errors for other computationally difficult, viscous microdevice flows being solved by the direct simulation Monte Carlo method.