An improved three-dimensional implicit discrete velocity method on unstructured meshes for all Knudsen number flows

Abstract

In this work, an improved implicit discrete velocity method (DVM) on unstructured meshes is developed for simulation of three-dimensional (3D) flows in all flow regimes. Different from the conventional DVM, in which only the kinetic governing equation (i.e., Boltzmann equation) is resolved in each time step, both the kinetic and macroscopic governing equations are solved simultaneously in the present method. On one hand, the solution of macroscopic governing equation yields the predicted equilibrium distribution function at cell center, which enables the fully implicit discretization of the collision term in solving the Shakhov-model kinetic equation. On the other hand, the collisional effect at the cell interface can be incorporated into the evaluation of numerical flux through the solution process of macroscopic governing equation. Thanks to these two improvements, the developed scheme can effectively overcome the defects of low efficiency and poor accuracy of the conventional semi-implicit DVM in the continuum flow regime. In addition, for practical applications of flow problems with complicated geometry, in the present work, the unstructured mesh-based solver is developed. The accuracy, efficiency, stability and flexibility of the developed solver are demonstrated by its application to simulate pipe flow, lid-driven cavity flow and supersonic flow around a blunt body.