Hybrid Continuum/Molecular Simulations of Transient Gas Flows with Rarefaction

An adaptively coupled continuum-molecular approach for compressible viscous flows in transient calculations is presented. The continuum domain is described by the unsteady compressible Navier-Stokes equations, and the molecular domain is solved by direct simulation Monte Carlo. A strategy is described to extend the overlapped Schwarz method with Dirichlet-Dirichlet boundary-condition coupling procedure to transient simulations. The method has been successfully validated against full direct simulation Monte Carlo results for transient simulations of a one-dimensional shock tube and a two-dimensional pressure-driven slit flow. A sensitivity analysis showed that the used overlapped Schwarz coupling method with Dirichlet-Dirichlet boundary conditions is only weakly sensitive to various parameters (e.g., the exact position of the continuum/molecular interface, the size of the overlap region, and the scatter in the molecular solution), which is a clear advantage over the more commonly used flux-based coupling technique. Another advantage of the chosen coupling method is that the continuum and molecular time steps can be decoupled and that, in general, a coupling time step can be used that is much larger than the molecular time step. The study performed also highlighted a limit of the method: it was found to be necessary to keep the Courant number (based on the coupling time step, the cell size in the continuum region, and the molecular most-probable velocity) below 1 to avoid instabilities. [PUBLICATION ABSTRACT]