Grad's distribution function for 13 moments-based moment gas kinetic solver for steady and unsteady rarefied flows: Discrete and explicit forms. (1st May 2023) - Liu, W.; Liu, Z.J.; Zhang, Z.L.; Teo, C.J.; Shu, C.
Abstract: Efficient modeling of rarefied flow has drawn widespread interest for practical engineering applications. In the present work, we proposed the Grad's distribution function for 13 moments-based moment gas kinetic solver (G13-MGKS) and the macroscopic governing equations are derived based on the moment integral of the discrete Boltzmann equation under the finite volume framework. Numerical fluxes at the cell interface related to the macroscopic variables, stress and heat flux can be reconstructed from the Boltzmann equation along the characteristic line directly. The initial distribution function is approximated by Grad's distribution function for 13 moments at the cell interface, so the explicit expression of numerical fluxes could be derived to release the present solver from the discretization and numerical integration in the molecular velocity space. The G13-MGKS with the discrete and explicit form of numerical fluxes are examined by several tests covering the steady and unsteady flows from the continuum regime to rarefied flow regimes. Numerical results indicate that the G13-MGKS could simulate continuum flows accurately and present reasonable predictions for rarefied flows at moderate Knudsen numbers. Moreover, the consumption of computations and memory demonstrates that the present framework could preserve high efficiency.