A Variant of Improved Discrete Velocity Method for Efficient Simulation of Flows in Entire Knudsen Number Regimes

Abstract

In this paper, a variant of the improved discrete velocity method (VIDVM) is proposed for flows in the whole Knudsen number regimes. This method retains the advantage of the improved discrete velocity method (IDVM), which calculates numerical fluxes through a self-adaptive strategy by combining the microscopic reconstruction and the macroscopic reconstruction. Like the IDVM, the microscopic reconstruction for VIDVM is also based on the collisionless Boltzmann solver. However, different from IDVM, the macroscopic reconstruction for VIDVM is established on the Euler solver instead of the Navier-Stokes solver. Considering that the Euler solver merely computes the inviscid fluxes while the Navier-Stokes solver additionally calculates the viscous fluxes, the present method could be more efficient than IDVM. To validate the accuracy and efficiency of the present scheme, some benchmark cases from the continuum regime to the free molecular regime are conducted. Results reveal that the present scheme can predict the flow as well as IDVM, but the present solver is more efficient than IDVM.

Keywords: discrete velocity method, collisionless Boltzmann equation, Euler equations, continuum regime to free molecular regime