Moment flux-based discrete velocity method based on the Boltzmann-BGK equations along the characteristic line

• A moment flux-based discrete velocity method (MF-DVM) based on the Boltzmann–BGK model is proposed. • Molecular transport and collision effects are accurately captured along characteristic lines. • Implicit coupling of microscopic and macroscopic equations accelerates convergence. • Macroscopic fluxes are derived from Grad’s 13-moment formulation for efficiency. • Validated in Rayleigh, cavity, airfoil, and sphere flows across all Knudsen regimes. This paper introduces an improved scheme based on the discrete velocity method. Specifically, the reconstruction of the velocity distribution function and numerical flux at the interface is founded on the solution of the Bhatnagar-Gross-Krook equation along the characteristic line. The proposed method accurately considers molecular transport and collision effects at the interface, thereby enabling accurate modeling from rarefied to continuum flow regimes. Additionally, the implicit discretization of the microscopic equations and incorporation of macroscopic equations result in accelerated convergence properties for steady-state problems. The proposed numerical approach is validated through several cases, including Rayleigh flow, lid-driven cavity flow, flow past an NACA0012 airfoil, and supersonic flow around a sphere. Numerical results demonstrate that the proposed method can efficiently and accurately obtain multiscale flow properties.