A Hybrid Particle Scheme for Simulating Multiscale Gas Flows with Internal Energy Nonequilibrium

Abstract

A hybrid particle scheme, which is based on the direct simulation Monte Carlo (DSMC) method and incorporates a low diffusion particle method for continuum flow simulation, is extended for improved efficiency and wider applicability. The hybrid scheme is intended for simulation of gas flows involving a wide range of Knudsen number regimes, where strong coupling is desired between calculations in rarefied and continuum flowfield regions. A series of modifications are presented for cell-based numerical weight and time step adaptation, diffusive transport of nonequilibrium internal energy modes, and decreased sensitivity to DSMC cell size. Proposed modifications are employed in a hybrid simulation of a Mach 20 flow around a cylinder with a global Knudsen number of 0.002, for which a factor of 2.6 efficiency increase relative to full DSMC computation is demonstrated. I. Introduction n a variety of gas flow problems, portions of the flowfield exhibit large translational nonequilibrium effects and require relatively expensive simulation techniques based on the Boltzmann equation, while other regions are within low Knudsen number (Kn) continuum flow regimes and can be prohibitively expensive to simulate using such Boltzmann equation techniques. These “multiscale” flow problems include flows around atmospheric entry vehicles and hypersonic aircraft, where local Kn values based on gradient length scales may be very small through much of the flowfield but become large within shock, forebody boundary layer and wake regions. Other examples include rocket exhaust plumes and fuel venting flows at high altitude, where the mean free path may differ by several orders of magnitude between nearfield and farfield regions. A. Simulation Methods for Multiscale Gas Flows Accurate simulations may be performed for some of these flows using a two step, one-way coupled approach. 1-3 In this type of approach, continuum and rarefied regions are considered independently and different simulation techniques are applied in each region. In general, however, effects of two-way coupling between rarefied and continuum regions must be considered, and a single simulation employing a coupled hybrid algorithm is required. In one popular type of hybrid algorithm, a computational fluid dynamics (CFD) technique based on the Navier-Stokes equations is used in low-Kn continuum regions, the direct simulation Monte Carlo (DSMC) method is employed in rarefied regions, and additional procedures are used for evaluation of continuum breakdown and two-way information transfer between CFD and DSMC calculations.