  A Kinetic Inviscid Flux (KIF) is proposed for simulating incompressible and
compressible flows. It is constructed based on the direct modeling of
multi-scale flow behaviors, which is used in the Gas-Kinetic Scheme (GKS), the
Unified Gas-Kinetic Scheme (UGKS), the Discrete Unified Gas-Kinetic Scheme
(DUGKS), etc.. In KIF, the discontinuities (such as the shock wave) that can
not be well resolved by mesh cells are mainly solved by the Kinetic Flux Vector
Splitting (KFVS) method representing the free transport mechanism (or
micro-scale mechanism), while in other flow regions that are smooth, the flow
behavior is solved mainly by the central-scheme-like Totally Thermalized
Transport (TTT). The weights of KFVS and TTT in KIF is automatically determined
by those in the theory of direct modeling. Two ways of choosing the weights in
KIF are proposed, which are actually the weights adopted in the UGKS and the
DUGKS, respectively. By using the test cases of Sod shock tube, rarefaction
wave, the boundary layer of flat plate, the cavity flow and hypersonic flow
over circular cylinder, the validity and accuracy of the present method are
examined. The KIF does not suffer from the carbuncle phenomenon, and does not
introduce extra numerical viscosity in smooth regions. Especially, in the case
of hypersonic cylinder, it gives a quite sharp and clear density and
temperature contours. The KIF can be viewed as an inviscid-viscous splitting
version of the GKS. By the doing this splitting, it is easy to be used in the
traditional CFD frameworks. It can also be classified as a new type in the
numerical schemes based on the kinetic theory that are represented by the works
in Ref. \cite{SunA} and Ref. \cite{ohwada2018a}, except the weights are
determined by the weights of direct modeling.
