A novel solver for simulation of flows from continuum regime to rarefied regime at moderate Knudsen number

• Published in: Journal of computational physics 2020-08, Vol.415, p.109548, Article 109548
• Main Authors: Liu, Z.J., Shu, C., Chen, S.Y., Yang, L.M., Wan, M.P., Liu, W.
• Format: Article
• Language: English
• Subjects: Boltzmann transport equation; Computational physics; Computer simulation; Conservation laws; Continuum and rarefied flows; Discrete velocity method; Distribution functions; Energy conservation; Finite volume method; Fluxes; Gas kinetic flux solver; Mathematical analysis; Moment method; Novel solver
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2020.109548

•It is the first time to present this new flow solver.•The new solver combines good features of discrete velocity method, gas kinetic flux solver and moment method.•It avoids solving a coupled and complicated set of partial differential equations for high order moments.•The solver is much more simple and stable than the conventional moment method.•It can simulate flows from continuum regime to rarefied regime at moderate Knudsen number. A novel and simple solver for simulation of flows from continuum regime to rarefied regime at moderate Knudsen number is developed in this work. The present solver combines good features of gas kinetic flux solver (GKFS), discrete velocity method (DVM) and the moment method. Like the GKFS, in the present solver, the macroscopic governing equations are discretized by finite volume method and the numerical fluxes at cell interfaces are evaluated by the local solution of Boltzmann equation. To get the local solution of Boltzmann equation, the initial distribution function is reconstructed with the help of Grad's distribution function, which is inspired from the moment method. For the high order moments in Grad's distribution function, they are computed directly by the moments of distribution function, which is inspired from DVM. In principle, the present solver only needs to discretize the physical space and solves the governing equations resulted from conservation laws of mass, momentum and energy. Thus, its governing equations are much simpler than those of the moment method. To validate the proposed solver, some test examples covering continuum regime and rarefied regime are simulated. Numerical results showed that the present solver can give accurate prediction in the continuum regime and reasonable results as the traditional moment method in the rarefied regime at moderate Knudsen number.