Stochastic methods for modeling hydrodynamics of dilute gases

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2006.Includes bibliographical references (leaf 18).When modeling small scale sub-micron gas flows, continuum methods, i.e. Navier Stokes equations, no longer apply. Molecular Dynamics (MD) approaches are then more appropriate. For dilute gases, where particles travel in straight lines for the overwhelming majority of the time, MD methods are inefficient compared to kinetic theory approaches because they require the explicit calculation of each particle's trajectory. An effective way to model the hydrodynamics of dilute gases is a stochastic particle method known as Direct Simulation Monte Carlo (DSMC). In DSMC the motion and collision of particles are decoupled to increase computational efficiency. The purpose of this thesis is to evaluate a variant of the DSMC algorithm, in which particles have discrete velocities. The most important modification to the DSMC algorithm is the treatment of collisions between particles with discrete velocities in a way which ensures strict conservation of momentum and energy. To achieve that an algorithm that finds all possible pairs of discrete post-collision velocities given a pair of discrete pre-collision velocities was developed and coded.(cont.) Two important discretization ingredients were introduced: the number of discrete velocities and the maximum discrete velocity allowed. A number of simulations were performed to compare the discrete DSMC (IDSMC) and the regular DSMC method. Our results show that the difference between the two methods is small when the allowed discrete velocity spectrum extends to high speeds. In this case the error is fairly insensitive to the number of discrete velocities used. On the other hand, when the maximum velocity allowed is small compared to the most probably particle speed (approximately equivalent to the speed of sound), large errors are observed (in our case up to 450% in the stress).by Tristan J. Hayeck.S.B