Improved discrete velocity method for diatomic molecules with rotational and vibrational non-equilibrium effects

The improved discrete velocity method (IDVM) is a multiscale simulation approach capable of modeling flow fields across the entire regime, from continuum to free molecular flows. Compared with the traditional discrete velocity method (DVM), IDVM retains the simplicity of the conventional formulation while significantly enhancing computational accuracy and efficiency in the near-continuum regime. In this work, the fully implicit IDVM was extended to the Boltzmann equation based on a phenomenological collision model to simulate cross-regime flows of diatomic gases with rotational and vibrational nonequilibrium effects. The solution of the macroscopic governing equations was coupled with the implicit discretization of the kinetic model equation, and the collision effect was incorporated into the interface flux reconstruction, thereby overcoming the inherent deficiency of the traditional DVM in computational efficiency in the continuum regime. Validation against benchmark problems across different dimensions and Mach numbers showed good agreement with comparable numerical methods and experimental data. In the continuum and near-continuum regimes, the computational cost is reduced by approximately one order of magnitude compared with the conventional semi-implicit DVM. Moreover, the inclusion of vibrational modes improves the predicted drag coefficient of a three-dimensional sphere from −1.19% to −0.67% relative to the experimental value. These results demonstrate that the proposed method can accurately and efficiently simulate non-equilibrium flow problems of diatomic gases.