A Hybrid CFD-DSMC Method of Modeling Continuum-Rarefied Flows

Abstract

A hybrid method of simulating high-speed, non-equilibrium flows solves the NavierStokes equations using a Computational Fluid Dynamics (CFD) model in regions of the flow where properties are continuous and a statistical Direct Simulation Monte Carlo (DSMC) model in regions where properties are non-continuous and thermal nonequilibrium exists. The hybrid method is designed to balance computational efficiency and accuracy by utilizing a relatively inexpensive CFD model whenever appropriate and the DSMC model in critical regions of thermal non-equilibrium. The algorithm uses locally computed values of a breakdown parameter to evaluate the continuum assumption and turns on the DSMC component when the parameter exceeds a threshold value. The DSMC algorithm utilizes the methods of Information Preservation (IP) and ghost cells to accurately and efficiently exchange macroscopic flow properties with the CFD algorithm. Comparisons are made between experimental data for argon flow in a shock tube at Mach numbers 1.55, 5.0, and 10.0 using three computational models—pure CFD, pure DSMC, and hybrid CFD-DSMC. At Mach 1.55, close agreement exists between the experimental data and all of the computational models. At Mach 5 and 10, non-equilibrium becomes significant through the shock layer, and the CFD results diverge from the experimental data. Close agreement exists between the experimental data and both the DSMC and the hybrid simulations at all three Mach numbers, demonstrating that the hybrid method accurately models both equilibrium and non-equilibrium flows. Currently, the hybrid model is more, rather than less, expensive than the pure DSMC model—as a result of limits on the maximum allowable time step size imposed by the IP algorithm. A primary objective of future work is to significantly reduce the computational expense of the hybrid method by incorporating a more robust IP formulation.