Development of a hybrid particle-continuum solver for studying plume expansion into rarefied flows

The direct simulation Monte Carlo (DSMC) method and unsteady Navier-Stokes (NS) are combined in a hybrid formulation with an ultimate aim to model positioning-rocket laminar jet expansion in the lunar atmosphere. The hybrid solver uses the Schwarz technique, a classical matching procedure of the length scales and time scales between the continuum and rarefied environments. The novelty of the current work is its ability to be applied to unsteady problems and to accommodate a large variation in Knudsen number values, Kn. The length scale coupling from the continuum to the DSMC region is determined by a criterion based on the local gradient-length of Kn, which according to the specified criterion is larger than the continuum breakdown parameter set at the value of 0.05 at the transition from continuum to rarefied conditions for a jet. To this end, one-dimensional steady shock configurations with upstream Mach numbers varying between 1.7 to 8.4 are studied. Perfect agreement is achieved with measurements, indicating that spatial coupling between the rarefied and continuum regions is performed precisely. To ensure time accuracy in the coupling, the number of DSMC time steps is determined by the ratio of the continuum (i.e., NS) time step to the DSMC time step, which is governed by the mean collision time of particles. A relatively good agreement between the measurement data and current work for unsteady shock motion indicates that the hybrid framework can model time-dependent flows accurately.