An unstructured direct simulation Monte Carlo methodology with Kinetic-Moment inflow and outflow boundary conditions

Abstract

The mathematical and computational aspects of the direct simulation Monte Carlo on unstructured tetrahedral grids (U3DSMC) with a Kinetic-Moment (KM) boundary conditions method are presented. The algorithms for particle injection, particle loading, particle motion, and particle tracking are presented. The KM method applicable to a subsonic or supersonic inflow/outflow boundary, couples kinetic (particle) U3DSMC properties with fluid (moment) properties. The KM method obtains the number density, temperature and mean velocity needed to define the equilibrium, drifting Maxwellian distribution at a boundary. The moment component of KM is based on the local one dimensional inviscid (LODI) boundary conditions method consistent with the 5-moment compressible Euler equations. The kinetic component of KM is based on U3DSMC for interior properties and the equilibrium drifting Maxwellian at the boundary. The KM method is supplemented with a time-averaging procedure, allows for choices in sampling-cell procedures, minimizes fluctuations and accelerates the convergence in subsonic flows. Collision sampling in U3DSMC implements the no-time-counter method and includes elastic and inelastic collisions. The U3DSMC with KM boundary conditions is validated and verified extensively with simulations of subsonic nitrogen flows in a cylindrical tube with imposed inlet pressure and density and imposed outlet pressure. The simulations cover the regime from slip to free-molecular with inlet Knudsen numbers between 0.183 and 18.27 and resulting inlet Mach numbers between 0.037 and 0.027. The pressure and velocity profiles from U3DSMC-KM simulations are compared with analytical solutions obtained from first-order and second-order slip boundary conditions. Mass flow rates from U3DSMC-KM are compared with validated analytical solutions for the entire Knudsen number regime considered. Error and sensitivity analysis is performed and numerical fractional errors are in agreement with theoretical errors. The KM method is shown to be a robust technique allowing efficient computation of subsonic flows. Additional verification of U3DSMC is achieved with simulations of the heat transfer process in a stationary argon gas between two flat plates. The numerical heat flux is in agreement with analytical results that cover the transitional to free molecular regimes. Additional validation of U3DSMC is achieved with simulations of hypersonic rarefied flows of nitrogen over a finite thickness flat pate at 0 and 10 degrees angle of attack. Numerical predictions of the pressure and heat flux to the plate are in agreement with experiments.