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.

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