Modified unified kinetic scheme for all flow regimes

A modified unified kinetic scheme for the prediction of fluid flow behaviors in all flow regimes is described. The time evolution of macrovariables at the cell interface is calculated with the idea that both free transport and collision mechanisms should be considered. The time evolution of macrovariables is obtained through the conservation constraints. The time evolution of local Maxwellian distribution is obtained directly through the one-to-one mapping from the evolution of macrovariables. These improvements provide more physical realities in flow behaviors and more accurate numerical results in all flow regimes especially in the complex transition flow regime. In addition, the improvement steps introduce no extra computational complexity.