  In this study, the kinetic inviscid flux (KIF) is improved and an implicit
strategy is coupled. The recently proposed KIF is a kind of inviscid flux,
whose microscopic mechanism makes it good at solving shock waves, with
advantages against the shock instability phenomenon. When developing the
implicit KIF, a phenomenon is noticed that the kinetic flux vector splitting
(KFVS) part in boundary layers not only reduces the accuracy, but seriously
reduces the Courant-Friedrichs-Lewy (CFL) number as well. As a result, in this
paper, a new weight is proposed about how to combine the KFVS method well with
the totally thermalized transport (TTT) method. Besides admitting the using of
larger CFL numbers, this new weight brings about more accurate numerical
results like pressure, friction coefficient and heat flux when solving shock
waves, boundary layers and complex supersonic/hypersonic flows. In order to
examine the validity, accuracy and efficiency of the present method, six
numerical test cases, covering the whole speed regime, are conducted, including
the hypersonic viscous flow past a cylinder, the hypersonic double-cone flow,
the hypersonic double-ellipsoid flow, the laminar shock boundary layer
interaction, the supersonic flow around a ramp segment and the lid-driven
cavity flow. The advantages of this scheme and corresponding mechanisms are to
be discussed in detail.
