Multiscale gas-kinetic simulation for continuum and near-continuum flows

Abstract

It is well known that for increasingly rarefied flow fields, predictions from continuum formulations, such as the Navier-Stokes equations, lose accuracy. The inclusion of higher-order terms, such as Burnett or high-order moment equations, could improve the predictive capabilities of such continuum formulations, but there has been only limited success. Here, we present a multiscale model. On the macroscopic level, the flow variables are updated based on the mass, momentum, and energy conservation through the fluxes. On the other hand, the fluxes are constructed on the microscopic level based on the gas-kinetic equation, which is valid in both continuum and near-continuum flow regimes. Based on this model, the nonequilibrium shock structure, Poiseuille flow, nonlinear heat conduction problems, and unsteady Rayleigh problem will be studied. In the near-continuum flow regime, the current gas-kinetic simulation is more efficient than microscopic methods, such as the direction Boltzmann solver and direct-simulation Monte Carlo method. In the continuum flow limit, the current formulation will go back to the gas-kinetic Navier-Stokes flow solver automatically.