On the stability of higher-order continuum (HOC) equations for hybrid HOC/DSMC solvers

Our interest in the stability analysis of the high-order continuum (HOC) equations is motivated by the relevance to the development of a hybrid method combining such equations with the Direct Simulation Monte-Carlo (DSMC) technique for the computation of hypersonic flows in all regimes - continuum, transition, and rarefied. The hybrid approach allows the effects of thermophysics (thermal and chemical non-equilibrium) and turbulence to be included much more easily than in other approaches, and can easily be developed into a robust and efficient engineering tool for practical 3D hypersonic computations. Stability characteristics of model HOC equations when subjected to small disturbances are investigated. We explore the feasibility of simplified, yet accurate and numerically stable, versions of the HOC equations and extend our previous work to include multidimensional Burnett equations, with the specific example of the Augmented Burnett models. The latter is shown to have a much wider stability regime than Lumpkin's model.