Kinetic hybrid method based on correction of N-S constitutive relation

As rarefaction effect becomes stronger for flight vehicles in the near space, the linear constitutive relation in the Navier-Stokes equations is not able to describe the transportation process of rarefied gas properly, while the high-order nonlinear constitutive relation is too complicated in its mathematical form, which can cause troubles, such as instability, for finding the numerical solutions. To tackle this issue, a kinetic hybrid method based on the correction of the linear constitutive relation has been proposed in the present study. In this method, the stress tensor and heat flux obtained from the Gas Kinetic Unified Algorithm (GKUA) are used to correct the linear constitutive relation of the Navier-Stokes equations such that it is capable to simulation flows with local rarefaction effects. The new method is validated by two testing cases, i.e., rarefied flows on a compressible flat-plate boundary layer and around a circular cylinder, respectively.