Conservative Supra-Characteristics Method (CSCM), a variant of Roe’s flux-difference splitting
formulation, was developed formerly as a viable engineering prediction tool for aerodynamic design
and had indeed shown its versatility in computing such complex flows as hypersonic/supersonic
jet interaction field. The method adopted the characteristic boundary conditions implicitly at the
boundary by identifying five characteristics embedded in the governing equations. But the lack
of consistency in formulation as well as its complexity deterred it to be a popular algorithm for
widespread use. In an effort to retain the characteristic boundary procedure associated with CSCM,
a flux-difference formulation has been devised that follows Roe’s linearization but formulates like
CSCM, decomposing the conservative Jacobian matrix into product of transformation matrices.
The latter enables one to recognize that the governing conservative equations are indeed another
form of characteristic equations, thereby clarifying the use of characteristics at the boundary.
The validity of current numerical method is demonstrated for wide range of flows. Accuracy of
solutions is enhanced through second-order extension in space, and shock instability is overcome
for 2-D flow as well as 3-D flow. Robustness of numerics is proven by capturing unsteady nature
of jet impingement through modification of dissipation terms in the Roe flux. With proper inflow
conditions, both mass flow rate and total pressure are also shown to be conserved for a nozzle flow.