Gas‐kinetic unified algorithm for plane external force‐driven flows covering all flow regimes by modeling of Boltzmann equation

다국어 초록 (Multilingual Abstract)

The nonequilibrium steady gas flows under the external forces are essentially associated with some extremely complicated nonlinear dynamics, due to the acceleration or deceleration effects of the external forces on the gas molecules by the velocity distribution function. In this article, the gas‐kinetic unified algorithm (GKUA) for rarefied transition to continuum flows under external forces is developed by solving the unified Boltzmann model equation. The computable modeling of the Boltzmann equation with the external force terms is presented at the first time by introducing the gas molecular collision relaxing parameter and the local equilibrium distribution function integrated in the unified expression with the flow state controlling parameter, including the macroscopic flow variables, the gas viscosity transport coefficient, the thermodynamic effect, the molecular power law, and molecular models, covering a full spectrum of flow regimes. The conservative discrete velocity ordinate (DVO) method is utilized to transform the governing equation into the hyperbolic conservation forms at each of the DVO points. The corresponding numerical schemes are constructed, especially the forward‐backward MacCormack predictor‐corrector method for the convection term in the molecular velocity space, which is unlike the original type. Some typical numerical examples are conducted to test the present new algorithm. The results obtained by the relevant direct simulation Monte Carlo method, Euler/Navier‐Stokes solver, unified gas‐kinetic scheme, and moment methods are compared with the numerical analysis solutions of the present GKUA, which are in good agreement, demonstrating the high accuracy of the present algorithm. Besides, some anomalous features in these flows are observed and analyzed in detail. The numerical experience indicates that the present GKUA can provide potential applications for the simulations of the nonequilibrium external‐force driven flows, such as the gravity, the electric force, and the Lorentz force fields covering all flow regimes.
1. The gas‐kinetic unified algorithm is developed for the plane external force‐driven flows covering the rarefied free‐molecule flow to the continuum flow regimes by the computable modeling of the Boltzmann equation. 2. The non‐equilibrium flow phenomena including the bimodal temperature, nonconstant pressure, flow velocity and heat flux profiles in the external force‐driven Poiseuille flows are revealed and analyzed by the current algorithm. 3. For the lid‐driven cavity flow under gravitational field, with an increase in rarefaction of Knudsen numbers Kn = 5 × 10−5 ∼ 10, both expansion cooling and gravity play greater roles in determining the heat transfer characteristics from the continuum to the free‐molecule flow regimes.