Motivation

Direct simulation Monte Carlo (DSMC) is a particle method that simulates the Boltzmann equation. The Boltzmann equation is the governing equation for dilute gases ranging from continuum to free-molecular conditions. The DSMC method is therefore able to accurately model non-equilibrium (low-density, rarefied) flows and is also accurate for continuum flows where it reproduces results from continuum computational fluid dynamics (CFD). The DSMC method tracks a large number of simulated gas molecules through a computational domain allowing for collisions between gas molecules and also collisions with surfaces. The main assumption inherent in the DSMC method is that molecular movement can be decoupled from molecular collisions (an accurate assumption for dilute gases). Simulated molecules are moved in a straight line for a timestep close to the local mean-collision-time. Afterwards, nearby particles (located within the same computational cell) are collided in a statistical manner. As long as the cell size is less than the mean-free-path (the average distance travelled between molecular collisions), and the collision rate/probability is chosen correctly, the DSMC method is able to accurately simulate real, complex gas flows.

Per cell, the DSMC method is only slightly more expensive than CFD, however, the restrictions of very small cells and small timesteps results in DSMC being quite expensive for near-continuum 3D flows. However, as parallel computing resources continue to rapidly grow, larger and more complex DSMC simulations become possible each year. Typical applications include computing the flow over low-orbit satellites, hypersonic planetary entry simulations, high-altitude high-speed vehicles as well as simulating rocket plumes, DSMC is also used in the manufacture process and function of micro-electromechanical systems (MEMS) as a result of gas flow at extremely small length scales where the molecular nature of the gas must be accounted for.

Results and Publications