An improved discrete velocity method (DVM) for efficient simulation of flows in all flow regimes

Abstract

In this paper, an improved discrete velocity method (DVM) is developed for efficient simulation of fluid problems in all flow regimes. Compared with the conventional explicit DVM, the present scheme could effectively remove its drawbacks of low accuracy and efficiency in continuum flow regime with no deterioration of its performance in rarefied flow regime. One of the novel strategies adopted in the new method is to introduce a prediction step for solving the macroscopic governing equation. By using the prediction step, the equilibrium state is first estimated before solving the discrete velocity Boltzmann equation (DVBE). As a result, the collision term in the DVBE can be discretized implicitly to improve the stability and efficiency of the conventional explicit DVM. Another contribution of the new method is to physically reconstruct numerical flux at the cell interface by incorporating the collision effect into the process. To maintain simplicity and efficiency of the conventional DVM, in the present scheme, the collision effect in the flux reconstruction at the cell interface is considered through the solution of the macroscopic governing equation. This can effectively control the effect of numerical dissipation in the process of updating the macroscopic flow variables in the continuum flow regime. Analyses indicate that the prediction step does not contribute to the evolution of distribution functions in the highly rarefied flow regime while dominating the solutions in the continuum flow regime. Accordingly, the improved scheme automatically converges toward the conventional explicit DVM in the free molecular flow regime and approaches the Navier-Stokes solver in the continuum flow regime.